RICHTBR'S 


MANUAL  OP  HARMONY: 


PRACTICAL  CTJIDE  TO  ITS  STUDY 


PBEPABRD    ESPECIAIJ.Y  rOB  THB 


CONSERVATORY  OF  MUSIC  AT  LEIPSIC. 


BY 


ERNST  FRIEDRICHj^JMCHTER, 

UNIVERSITY  MUSIC-DmECTOR,   ORGANIST  OP  THE  CHURCH  OP  ST.  NICOLAI,   AND  Df- 
STRUCTOR  IN  THE  CONSERVATORY  OP  KUSIC. 


TKANSLATED  FROM  THE  LATEST  GERMAN  EDITION 

By  JOHN  P.  MOKGAN, 

ALUMNUS  OP  THE  LEIPSIC  CONSERVATORY   OP  MUSIC,   AND    PUPIL  OP   THE   AUTHOB, 

FIFTH   jEDITION. 

NEW    YOUK: 
Q.  SCHIRMER,   701  BROADWAY. 


^u%,€.    VeT^TT 


Ent«recl>  according  to  Act  of  Congress,  in  the  year  ISOT,  by 

w,    btiiililMEli 

t»  the  Clerk's  Office  of  the  District  Conrt  of  the  United  States  for  the  Northern  District  of  New  York 


stereotyped  by  Smrn  &  McDotra^T  82  &  8A  Beekmsn  St. 


^^  ■  Mr  so 


TEANSLATOR'S    PREFACE, 


In  offering  to  the  American  public  this  translation  of  Eichter*8 
Harmonielehre  we  need  have  no  hesitation  in  saying,  that  we 
offer  a  translation  of  the  best  text-hook  of  Harmony  which  has,  as 
yet,  been  given  to  the  world. 

No  one  knows  better  than  its  author  the  road  which  one  must 
take  to  become  21.  practical  harmonist ;  and  no  one  has  been  more 
successful  in  leading  pupils  to  real  success. 

The  Manual  contains  the  outlines  of  the  course  w^hich  has 
proved  itself  the  best  during  his  many  years  of  efficient  labor  as 
Instructor  in  Harmony  in  the  Conservatory  of  Leipsic  ;  and  the  im- 
mense sale  the  work  has  had  in  Europe,  shows  in  what  estimation 
it  is  held  by  the  musical  public. 

A  few  remarks  as  to  the  translation : — Every  one  who  is  at  all 
acquainted  with  the  matter,  knows  how  exceedingly  difficult  it  is 
to  do  justice  to  a  German  scientific  work  in  an  English  translation ; 
and  in  no  science  is  the  poverty  of  exact  and  definite  English  terms 
greater  than  in  that  of  music. 

The  translator  has  striven  to  give,  throughout,  the  exact  sense 
of  the  original,  without  any  embellishment  for  the  sake  of  attrac- 
tiveness, and  has  always  preferred  a  square-cut  sentence  containing 
the  idea  of  the  original  in  fuU,  to  a  more  smoothly-rounded  one 
which  would  omit  or  add  something. 

A  few  clauses  or  words  which  seemed  necessary  for  clearness, 
have  been  enclosed  in  square  brackets. 

The  whole  work  has  been  performed  as  a  pleasant  dutv  to  a 


IV  TBANSLATOR    S     PEEFACE. 

teaclier  to  whom  the  translator  owes  all  gratitude,  and  in  behalf 
of  the  many  earnest  students  in  this  country,  who  are  utterly  with- 
out an  adequate,  'practical  Manual  of  Harmony  and  Introduction  to 
Counterpoint. 

Thanks  are  especially  due  to  his  revered  father,  Eev.  John 
Morgan,  D.  D.,  of  Oberlin  College,  for  his  kind  assistance  in  the 
vv  ork,  which,  without  the  aid  of  his  comprehensive  knowledge  of 
language  in  general,  and  of  the  German  in  particular,  must  have 
been  done  much  less  accurately. 

JOHN  P.  MOEGAN. 
New  York,  June  1«<,  1867. 


FROM  THE  PREFACE  TO  THE  FIRST  EDITION. 


The  most  immediate  occasion  for  publishing  this  text  book  of 
harmony  is  indicated  in  the  title.  It  was  desirable,  in  connec- 
tion with  the  practical  course  of  studies  in  the  theory  of  music, 
to  put  into  the  hands  of  the  pupils  a  help  for  the  explanation  of 
the  doctrines  brought  forward,  and  for  their  repetition.  The  quali- 
ties of  such  a  manual,  the  author  beHeves  to  be  these :  It  must 
contain  the  most  essential,  fundamental  part  of  the  musical  t7i£ory  ex- 
pressed in  a  manner  brief  but  as  complete  as  possible  ;  there  must  be 
these  fundamental  features  always  accompanied  by  reference  and 
guidance  to  the  practical  application,  in  order  to  qualify  for  later 
attempts  at  composition. 

The  book  contains  no  scientifically  theoretic  treatise  on  har- 
mony, but,  although  as  far  as  is  the  case  with  any  system  of 
harmony,  it  is  supported  upon  a  firm  basis,  is  only  dedicated  to 
the  practical  object,  which  with  the  scanty  means  now  accessible, 
would  be  very  difficult  to  attain  in  an  abstractly  scientific  way. 

There  has,  indeed,  ever  been  a  disposition  to  inquire  after  a 
mathematical  definiteness  in  musical  rules,  and  especially  youth, 
opposed  to  the  belief  in  authority,  would  like  to  have  everything 
so  clear  that  no  doubt  would  be  possible,  much  as  it  shrinks  on  the 
other  side, from  learning,  by  means  of  the  anatomical  knife,  to  know 
and  understand  the  blooming  life  of  art ;  and  it  is  not  to  be  denied 
that  in  this  respect  a  want  is  found  in  musical  literature,  which 
no  one  has  as  yet  entirely  succeeded  in  supplying.    All  attempts 


VI  PREFACE. 

of  the  sort  have  as  yet  failed  to  create  a  really  tenable  scientifi- 
cally musical  system,  according  to  which,  through  one  fundamental 
principle  all  phenomena  in  the  musical  realm  are  found  exhibited 
as  always  necessary  consequences,  and  what  philosophers,  mathe- 
maticians and  physicists  have  accomphshed  in  this  regard,  ii^ 
indeed  worthy  of  attention,  but  in  part,  too  much  divided  into 
isolated  portions  to  allow  the  easy  discovery  of  the  connecting 
links  for  the  completion  of  the  whole,  in  part,  too  abstract,  serving 
music  itself  less  than  other  objects,  and  with  all  the  understanding 
of  musical  things  shown  in  it,  still  having  little  reference  to  the 
properly  musical,  which  is,  after  all,  of  the  most  immediate  im- 
portance with  the  musician.  "What  is  laid  down  in  musical 
text  books  of  a  scientific  basis,  has  not,  however,  hitherto  verified 
itself,  because  it  in  part  as  application  of  single  learned  investiga- 
tions, was  just  as  little  able  to  create  a  system  complete  in  itself, 
with  indubitable  conclusions,  and  in  part,  as  a  fanciful  structure, 
was  utterly  without  scientific  basis.  * 

Still,  rightly  regarded,  this  deficiency  is  perceptible  only  to  the 
riper  and  educated  musician,  who  likes  to  busy  himself  with  theory, 
not,  however,  so  disadvantageous  to  the  advancing  student  of  music 
that  his  immediate  education  must  suffer  in  consequence  of  it ;  and 
this  scepticism,  referred  to  above,  might  be  compared  in  a  certain 
measure,  with  that  childish  mode  of  procedure,  which  from  over 
great  curiosity,  would  get  at  the  origin  of  all  things  through  ques- 
tions which  seldom  can  be  answered  comprehensibly  enough  for 
the  questioner's  stage  of  education.  The  advancing  student  of 
music  has  to  apply  his  whole  power  to  his  technical  education, 
because  it  will  cost  him  time  and  trouble  enough  to  attain  the 
stand-point,  starting  from  which  he  can  with  greater  ease  advance 
towards  the  position  of  a  real  artist.  Here  the  question  to  be 
asked  is  not  JVhy  ?  the  inquiry  of  immediate  application  is,  Hoto  ? 


*  It  may  here  be  permitted  to  call  attention  to  a  work  which  might  be  adapted  to 
meet  a  palpable  want:  Die  Natur  dot  ffarmonik  und  Metrik  by  M.  Havptmann. 


I 


PBEFACE.  m 

The  thing  to  be  done  is,  from  experience,  from  the  best  models,  to 
understand,  not  to  calculate,  the  necessity  of  certain  principles ; 
Idter,  if  education,  acquirements,  capability  and  calling  require  it, 
it  will  be  time  enough  to  investigate  the  why,  and  all  knowl- 
edge obtained  from  experience  will  be  an  aid  not  to  be  despised, 
for  discovering  also  the  laws  of  nature  pertaining  to  music. 

This  practical  aim  in  view,  the  author  was  at  pains  to  give  the 
exhibition  of  harmony,  and  of  the  propositions  resulting  from 
observation  and  experience,  in  a  simple  and  clear  manner,  and  since 
he  destined  the  book  for  study,  io  let  the  truths,  perhaps  contained 
in  it,  work  through  themselves ;  without  wishing,  through  an  espe- 
cially learned  dress  or  an  attractive  form,  to  obtain  for  them  an 
extended  circle  of  readers.  It  contains  the  doctrine  of  harmony 
complete,  with  hints  for  a  rational  method  of  performing  exercises, 
for  the  fixing  of  the  whole,  and  for  the  ready  carrying  out  of  aU 
harmonic  principles.  These  exercises  extend  to  the  beginning  of 
contrapuntal  studies ;  the  doctrine  of  counterpoint  itself  will  fol- 
low, however,  in  a  later  volume  after  the  same  plan. 

In  closing,  still  a  word  to  the  disciple  of  art ;  an  earnest  onoj 
indeed,  but  well  meant. 

It  is  our  object  to  reach  a  distant  goal ;  this  goal  is  the  actual  pro- 
duction of  works  of  art.  For  this  a  vigorously  exercised,  enduring 
activity  is  necessary,  to  comprehend  the  musical  principles,  to 
form  that  which  is  won  and  recognized  into  structures  capable  of 
life.  Those  will  bitterly  deceive  themselves,  who,  filled  with  the 
works  of  our  great  masters,  gifted  with  a  poetic  mind,  think  to  be 
able  to  pluck  the  blossoms,  without  learning  thoroughly  to  know 
and  prove  the  technical  aids ;  who  are  of  the  erroneous  opinion 
that  the  consecration  of  beauty  which  extends  itseK  over  the  work 
of  art  suffers  under  the  dissection  of  the  material,  or  that  the  first 
natural  formations  of  the  latter  could  never  develop  themselves 
to  that  requisite  beauty.  No  person  of  talent  has  ever,  without 
thorough  knowledge  (to  attain  which  was,  to  be  sure,  easier  to 
him  than  to  the  less  gifted),  risen  to  that  height,  upon  which  alone 


TUl  PREFACE. 

the  achievements  of  art  thrive.  Exercise  without  consciousness 
is  not  artistic  skill,  it  is  only  the  working  of  the  instinct,  which 
will  always  make  the  want  of  a  complete  education  sensible.  The 
spiritual  thought  cannot  do  without  the  form,  and  it  is  this  which 
must  be  recognized  and  learned.  Even  if  it  often  comes  with  the 
conception  of  itself,  still,  \\ith  music,  more  than  with  anything 
else,  it  is  of  importance,  as  it  were,  logically  to  dissect  the  thought, 
to  remodel  it  into  new  forms,  to  transform  it  in  the  most  manifold 
manner.  The  knowledge  of  these  things  and  skill  in  them  must 
be  acquired  by  the  person  of  talent  also,  and  this  can  only  be 
attained  by  taking  pains  to  recognize  the  musical  laws,  and  en- 
deavoring to  imitate  and  extend  what  others  have  abeady  long 
since  discovered.  Earnest,  persevering  activity,  and  above  all,  a 
rational  method  for  the  development  of  maturity,  for  the  forma- 
tion of  works  of  art  capable  of  life,  will,  in  connection  with  musical 
qapacity,  certainly  lead  to  the  goal 


FROM  THE  PREFACE  TO  THE  THIRD  EDITION, 


Although  in  tlie  present  edition  also,  the  methodical  order  of 
the  former  ones  has  been  retained,  still  it  has  received  material 
additions.  The  exercises  for  many  subjects  of  instruction  have 
been  increased  in  number,  where  it  seemed  necessary. 

As  concerns  the  last,  some  books  have  appeared  lately  which 
are  in  a  measure  related  to  the  present  manual,  viz :  Genercdhass- 
Uehtingen  nebst  Kurzen  Erlauterungen  by  Benedict  Widmann,  and 
Uebungen  zum  Studium  der  Earmonie  und  des  ConfrapunkfeSy  by 
Fekd.  Htller. 

Although  this  is  not  the  place  to  speak  more  particularly  of 
these  works,  still  let  me  here  be  permitted  to  thank  these  authors 
for  their  friendly  reference  to  my  work,  and  to  make  the  following 
additional  remarks  in  respect  to  it.  Although  the  study  of  the 
theory  of  music  through  the  so-called  thorough-bass  doctrine  has 
long  since  yielded  to  a  more  rational  method,  stiQ  the  thorough-bass 
figuring,  as  means  to  the  end,  has  to  me  proved  itself  too  excellent, 
to  admit  of  my  not  using  it  for  the  first  exercises  in  harmonic 
connections,  as  in  general  for  the  first  applications  of  harmonic 
knowledge.  A  farther,  more  extended  use  of  this  has  not  been 
made  in  my  text  book  itself,  but  in  the  first  of  the  works 
above  referred  to,  and,  indeed,  for  exercises  which,  in  part  follow 
the  course  of  my  text  book,  in  part  aim  at  other  practice.    The 


X  PEEFACE. 

work  of  HiLLEK,  however,  besides  the  exercises  which  professedly 
follow  the  xjourse  of  my  text  book,  offers  in  general  a  rich  material 
for  elaborations  of  the  most  manifold  kind,  not  alone  for 
harmonic  exercises,  but  for  all  branches  of  theoretic  musical  edu- 
cation. 

Since  the  exercises  in  my  text  book  could  not  of  course  be 
exhaustive,  and  are,  for  the  most  part,  given  only  in  a  suggestive 
way  in  order,  when  needed,  to  design  others  after  them,  both  works 
may  here  be  highly  recommended  for  this  object. 


-    PREFACE  TO  THE  FIFTH  EDITION. 

It  has  been  my  endeavor  in  this  fifth  edition,  also,  which 
became  necessary  in  a  short  time  after  the  fourth,  through  addi- 
tions, in  part  through  altered  verbal  expression,  to  attain  that 
perspicuity,  which  a  text  book  of  this  kind  must  possess,  if  it  ful- 
fill its  end  completely.  If  I  may  also  venture  to  hope  that  the 
book  has  been  in  many  directions  serviceable  and  of  use,  I  am 
still  conscious,  that  in  order  to  reach  the  simple  and  luminous 
representation  which  is  my  ideal,  many  an  improvement  is  still  to 
be  introduced.  This  edition,  however,  does  not  differ  essentially 
from  the  preceding,  and  I  wish,  that  beside  the  old  friends,  this 
new  edition  may  gain  for  itself  new  ones. 

ERNST  FEIEDE.  EICHTER. 

Leipsic,  DecemleTy  1863. 


TABLE    OF    CONTENTS. 


PAoa 
ISfTBODVCTioN.— Intervals, .      13 


PART    I. 

THE  FUNDAMENTAL  HARMONIES  AND  THE  CHOEDS  DERIVED  FROM  THEM. 

CHAPTER 

I.— -The  Triads  of  the  Major  Scale, 21 

II.— The  Triads  op  the  Minor  Scale, 40 

III. — The  Inversion  of  the  Triads, 47 

IV. — Harmonies  op  the  Seventh  {Vierldange),          ....  54 

V. — The  Inversions  op  the  Chord  op  the  Seventh,        ...  59 

VI.— Secondary  Harmonies  op  the  Se^t^nth, 64 

VII.— The  Inversion  of  the  Secondary  Chords  op  the  Seventh,    .  78 
VIII.— The  Chords  op  the  Seventh  in  connection  with  Chords  op 

Other  Tone-degrees, 81 

IX.— On  Chords  op  the  Ninth,  Eleventh  and  Thirteenth,        .  88 
X. — Chromatic  Alteration  op  the  Fundamental  Harmonies.    Al- 
tered Chords,           91 

XI.— On  Modulation  op  a  Passage  op  Music,       .       «...  103 


PART    II. 

ACCIDENTAL  CHORD  FORMATIONS.        TONES   FOREIGN  TO  THE  HARMONY. 

XII.— Suspensions, 105 

XHI.— The  Okgan-Point.     Stationary  Voices, 123 


XII  CONTENTS. 

OHAPTEX  TAOr 

XIV.— Passing  Notes.     CHANOiNa  Notes, .128 

XV.~Passing  Chords, 138 

XVI.— On  the  Means  for  Modulation, 141 


.       PAKT    III. 

PEACTICAL     APPLICATION     OF     THE     HARMONIES.       THE    EXERCISES    IN 
THEIR  USE  IN  THE  PURE  HARMONIC  STRUCTURE. 

XVII. — The  Simply  Harmonic  Accompaniment  to  a  Given  Voice,       .  157 

XVIII.— Extension  of  the  Harmonic  Accompaniment,          .       .       .  173 

XIX.— On  the  Development  of  Melody, 176 

XX. — On  Development  of  the  Accompanying  Voices,      ...  183 

XXI. — The  Exercises  in  the  Three-voiced  Movement,        .       .       .  187 

XXII.— On  the  Two-voiced  Movement,    . 193 

XXIII. — Harmonic  Elaboration  op  a  Given  Voice  in  Melodic  Devel- 
opment,   195 

XXrV.— The  Five-voiced  Movement, 203 

XXV. — The  Six,  Seven  and  Eight-voiced  Mo^tement,     .       -       .       .  206 

XXVI.— On  the  Musical  Forms  of  Close,          213 

Index  op  Subjects, 216 


A^ 

V 


-/.^    '"  y.  -^ 


s-/ 


INTRODUCTION. 


k 


Of  the  elementary  knowledge  for  -which  general  instruction  in  music 
provides,  and  acquaintance  with  which  must  be  presupposed  at  the 
beginning  of  the  study  of  harmony,  the  portion  which  stands  in  the  nearest 
relation  to  it,  viz :  The  Theory  of  Intervals,  will  be  treated  of  prelimina- 
rily in  a  brief  and  condensed  manner. 

Intervals.  I 

The  relation  in  which  one  tone  stands  to  another,  in  respect  to  differenc3 
of  pitch,  is  called  Interval. 

The  greatness  of  the  difference  is  directly  determined  according  to  the 
number  of  the  degrees  of  the  staff,  upon  which  the  two  tones  stand,  in 
respect  to  each  other,  and,  as  a  rule,  in  such  a  manner  that  the  lowest  tone 
is  reckoned  as  standing  upon  the  first  degree,  and  the  higher  is  determined 
according  to  the  number  of  diatonic  degrees  lying  between. 

R  EMAEK. — ^By  diatonic  degrees  ia  understood  the  series  or  progression  of  tones  pre- 
sented by  any  major  or  minor  scale. 

If  we  take,  for  example,  g  as  lower  tone,  and  situated  upon  the  first 
degree,  then  the  a,  being  the  higher,  will  come  upon  the  second,  the  e, 
higher  still,  upon  the  sixth  degree : 

«^- 

&c. 

The  numbers  of  the  degrees  produced  thus,  will  be  expressed  in  the 
following  manner : 

1  2345678 

i 


•^»'  ^         ^         ^         .^  ^  ^         .^ 

Unison  or  Prime.  Secon<J.     Tldrd.       Fourth.       Fifth.         Sixth,       Seventh,    Octane. 


14  MANUAL    OF   HARMONY. 

As  a  rule,  we  reckon  only  to  the  octave,  and  begin  the  series  again  with 
the  tones  which  lie  above,  and  so  on  with  each  new  octave,  so  that  the 
ninth  degree  becomes  a  second^  the  tenth  a  third,  the  eleventh  afourthj 
and  so  on ;  just  so  the  fifteenth  becomes  the  octave,  the  sixteenth  the 
second  again. 

Reasons,  however,  which  find  their  explanation  in  the  principles  of 
harmony  and  theory  in  general,  give  now  and  then  occasion  for  designat- 
ing tones  which  lie  above  the  octave,  according  to  the  actual  number  of 
the  degrees.  The  series  of  intervals  from  the  octave  upwards  will,  there- 
fore, receive  the  following  double  designation  : 

Octave.     Jfinth.      Tenth.     Eleventh.     Twelfth.    TIdrteenVi.    Fourteenth.    Fifteenth. 

.^u.  JS.  ^ 


:ar=: 


•^              •»              -^                 'A^                 -^  •»                      -^  •» 

Second.     Third.       Fourth.        Fifth.  SixtJu            Seventh.  Octave. 

Greater  distances  between  two  tones,  are  simply  reduced  to  their  rela 
tion  in  the  lower  octave. 


More  Particular  Deterniination  of  the  Intervals, 

It  is  easy  to  see  that  the  above  presentation  of  the  intervals,  is  based 
upon  the  diatonic  major  scale  of  C,  and  that  the  relations  of  the  tones 
which  lie  between  are  not  affected  thereby.  In  like  manner,  they  are  re- 
garded throughout,  as  based  upon  the  Jlrst  tone  of  the  diatonic  scale, 
whereas,  it  is  conceivable  that  any  tone  of  the  scale  can  be  taken  at  pleas- 
ure as  lower  tone,  whereby  the  numbers  of  the  degrees  would  be  altered, 
and  at  the  same  time,  small  differences  in  the  degrees  themselves  appear. 

In  order  to  gain  a  clear  view  of  the  matter,  in  the  midst  of  these  mani- 
fold variations,  it  will  be  well  to  note  carefully  the  following  principles  : 

The  series  of  intervals  shown  above,  in  which  the  lowest  tone  is  first 
tone  of  the  major  scale,  which  forms  the  series  itself,  serves  as  foundation 
for  all  determinations  of  intervals.  These  intervals  are  called  majori 
so7ne  of  them  perfect. 

Every  chromatic  alteration  of  these  tones,  of  the  upper  tone  as  ivell  as 
of  the  lower,  not  changing  the  number  of  the  degrees,  consequently  does  not 
alter  their  designation,  but  only  renders  a  more  particular  determination 
of  them  necessary. 

Thus,  for  example,  if  to  the  fifth  ^  a  sharp  is  m  any  .way  attached,  it 
remains  always  o. fifth,  but  requires,  however,  a  more  particular  determina- 


MANUAL    OF   HARMONY. 


15 


tion,  since  it  has  evidently  become  a  diferent  fifth  from  what  it  was  orig- 
inally. 


Or, 


Since  now  such  alterations  of  the  intervals  take  place  through  chromati- 
cally raising  or  lowering  them,  the  following  various  and  more  definitely 
determinative  designations  are  made  use  of : 

1.  Seconds,  thirds^  sixths,  sevenths  and  ninths,  which  result  from  the 
major  scale,  taking  its ^rs^  tone  for  lower  tone,  are  called  major;  primes, 
fourths,  fifths  and  octaves  perfect., 

•    2.  If  the  upper  tone  of  the  major  intervals  be  lowered  a  small  half-step, 
minor  intervals  result. 

3.  If  the  upper  tone  of  [most]  major  and  'perf^t  intervals  be  raised,  a 
small  half-step,  augmented  intervals  result. 

4.  If  the  lower  tone  of  most  perfect .  and  minor  intervals  be  raised  a 
half-step,  diminished  intervals  result. 


Tol. 

Perfect      Major       Major      Perfect      Perfect      Major      Major      Perfect      Major 


-'^ 


-^- 


Prime.    Second.      Third.       Fourth.      Fifth.       Sixth.      Seventh.     Octave.     Xi7it?t, 


To  2. 


Minor 


Minor 


Minor 


Minor 


Minor 


Second. 


Ihird. 


■Ms: 


:^ 


■P^ 


Sixth. 


To  3. 


I 


A  ugmented 


Augmented    *    Augmented 


Seventh. 


Augmented 


NintJi. 


Augmented 


'^ i!% — 


¥ 


;p 


PHme. 


Second. 


Fourth. 


Fifth. 


Sixth. 


To  "4. 


Diminished  Diminished         Diminished  Diminished         Diminished 


-^- 


Third. 


Fourth. 


L^=i 


Fifth. 


Seventh. 


Octave, 


•Augmented  thirds,  sevenths  and  ninths  do  not  occur  in  harmonic  relations.    Aiig 
mented  octaves  are  to  be  regarded  as  augmented  primes. 


16 


MANUAL    OF   HARMONY. 


Remark. — Diminished  primes,  seconds,  sixths  and  ninths,  are  harmonically  inoon- 
ceivable,  although  they  can  be  conceived  of  in  melodic  relations,  i.  e.,  in  reference  to 
progressing  intervals,  not  to  those  which  sound  together. 

Remark  on  the  Formation  of  the  Diminished  Intervals, 

The  reason  "why,  in  the  formation  of  the  diminished  intervals,  the  lower  tone  has  been 
raised,  notwithstandbg  that  a  like  interval  would  result,  if  the  upper  tone  were  low- 
ered, lies  in  the  peculiar  relations  of  all  the  intervals  in  regard  to  their  inversion,  which 
will  be  spoken  of  farther  on. 

General  Vieiv  and  Classification  of  the  Most  Used  Intervals, 


Primes. 
Perfect.  Augmented. 


3fajor. 


Seconds. 
Minor.  Augmented. 


*— l'*- 


-8*- 


1 


Major. 


Thibds. 
Minor. 


Diminished. 


Perfect. 


Fourths. 
Augm,6nted.       J[>iminished. 


-^•-^-|^r-^-E-:^: 


:#t 


m 


Fifths. 
Perfect.  Augmented.      Diminished.  Major, 


Sixths. 
Minor.  Augmented. 


$ 


mm 


izzzijzi 


¥ 


1=FF 


Sevenths.  Octaves.  Ninths. 

Major.  Minor.       Diminished.      Perfect.      Diminished.     Major.  Minor. 


fe=^=^-^'i^: 


m 


F 


r 


Division  of  the  InteiwaJLs  into  Consonances  and  Dissonances, 

If  we  speak  in  music  of  consonant  and  dissonant  intervals,  we  under- 
stand thereby,  not  well  or  ill  sounding  ones,  which,  to  be  sure,  can  be 
expressed  by  these  two  words,  but  by  the  first,  we  understand  such  as 
stand  in  a  pure,  satisfying  relation  to  each  other,  which  does  not  require  a 
certain  farther  connection  with  other  intervals ;  by  the  last,  such  as  defi- 
nitely indicate  a  farther  progression,  and  without  it  would  have  no 
satisfying  sense. 

The  consonances  comprise  all  those  intervals  called  perfect^  and,  in  ad 
dition,  the  mayor  and  minor  ihirds  and  sixths. 


MANUAL    OF   HARMONY. 


n 


% 


The  first  are  called  complete  consonances,  the  ?ast  incomplete. 
The  dissonances  are  the  major  and  minor  second,  major  and  minor 
seventh,  and  all  augmented  and  diminished  intervals. 
From  this  we  derive  the  following  general  plan  : 


I.  CONSONANCES. 
a.  Complete, 
The  perfect  prime,  perfect  fourth,  perfect  Jifth  and  perfect  octave. 
1  4*5  8 


mmii 


■^         ■»         19- 

h.  Incomplete. 
The  major  and  minor  third,  and  the  major  and  minor  sixth. 


5^fl 


II.  DISSONANCES. 


The  augmented  prime^  the  major,  minor  and  augmented  second,  the 
•diminished  third,  the  augmented  and  diminished  fourth,  the  augmented 
and  diminished  fifth,  the  augmented  sixth,  the  major,  minor  and  dimin 
ished  seventh,  the  diminished  octave,  and  the  major  and  minor  ninth. 


Augmented   1  Major.       Minor.         Aug.    2  Dimin.  3 


^ 


-%; — ^^? |%r 


i 


Aug. 


Dimin.    4 


^wgr. 


Dimin.  5 


-dli^r.      6 


%^ 


;6iE^E=i^:E^a^E^[^fe 


1 


I 


Major.     Minor.     Dimin.  7       Dimin.  8         Major.      Minor.  9 
b=1= "S* fe 


-^ ^ ;■ 


-r 


-F 


W 


•Later  in  the  instruction  in  harmony,  follows  a  farther  explanation  i>f  the  peculiar 
relations  of  ihQ  fourth. 


18 


MANUAL    OF    HARMONY. 


Inversion  ( Versetzung)  of  the  Intervals, 

As  was  already  indicated  above,  in  determining  the  intervals  we  begin 
as  a  rule,  with  the  lower  tone.  If,  however,  there  is  occasion  to  determine 
the  relation  of  two  tones,  taking  the  upper  tone  as  the  starting  point,  the 
intervals  found  are  called  intervals  below. 


Thus,  for  examp'Cj 


I 


is  d,  the  fifth  from  g  ;  g,  however, 


from  dj  the  fifth  helow.  It  is  easy  to  see  that  the  interval  cannot  be  al- 
tered by  this. 

It  becomes  different,  however,  if  the  upper  interval  be  removed  below 
the  original  lower  tone.  Since  particular  reference  is  had  to  this  inversion 
in  various  kinds  of  composition,  an  explanation  of  it  may  follow  here. 

The  diatonic  major  scale  will,  by  means  of  this  inversion,  assume  the 
following  form : 


Intervals  above :   1 


6 


7 


'Ji^^ 


-gg^- 


J: 


j^9i 


1 


InUrvaUheloxD :  8  7  6  5  4  3  2 

There  result  thus,  the  following  series  of  numbers : 


that  is,  through  inversion,  the  'prime  becomes   an  octave^  the  second  a 
seventh^  &c. 

The  inversion  of  the  major  scale  forming  the  basis,  we  must  note  the 
following  in  respect  to  all  intermediate  intervals : 

V  1.  All  PERFECT  intervals  remain    perfect  in    the  inversion  in  the 
Ipctave. 
\/   2.  All  MAJOR  intervals  become  minor,  all  minor  major,  the  augmented 
ODIMINISHED,  and  the  diminished  augmented. 

In  the  following  table  is  exhibited  a  view  of  all  the  inversions : 


Original 
Intkrvals. 


Imtersion. 


Primes. 
Perfect.         Augmented. 


|Ei'gE^EgEEg^^^ 


Major. 


Seconds. 
Minor. 


Augmented. 


£ 


iz::zs:i 


m 


OCTAVBS. 

Perfect          Diminished. 


3finor. 


Sevenths. 
Major. 


Diminithed. 


■^- 


.^_D hs 


MANUAL    OF   HARMONY. 


19 


FouETns. 
Augmented,      Diminished . 


Major.  Minor.       DiminisTied,        Perfect.  Augmented.      Diminished. 


Minor. 


Sixths. 
Major.       Augmented. 


Perfect. 


Fifths. 
Diminished.     Augmented. 


■^^^^^^^^^^^l 


Fifths. 
Perfect.  Augmented.    Diminished. 


-t- 


f- 


Major. 


Sixths, 
Minor. 

it 


Augmented. 


Perfect. 


FOPETIIS. 

Dimiiiished.    Augmented.         Minor. 


Thirds, 

Major.  Diminished. 


^^^=^1^=^^^^^^^^:^^^^^ 


Major. 


Sevenths. 
Minor. 


Diminished. 


Octaves. 
Perfect.  Diminislied. 


ipzzx 


i^ii 


m 


_<2- 


Minor. 


Seconds. 
Major, 


Augmented. 


Peimes. 
Perfect.  Aicgmented. 


•=F= 


fe-^^^ 


An  exact,  certain  knowledge  of  this  essential  inversion  of  the  intervals 
is  not  alone  important  for  the  exercises  in  double  counterpoint,  but  greatly 
facilitates  comprehension  and  insight,  in  simple  harmonic  structure,  for 
■which  reason  their  study  is  urgently  to  be  recommended. 

A  few  more  remarks  may  follow  here : 

/      The  reason  why,  in  the  first  table  of  intervals,  (page  16),  all  diminished 

intervals  were  formed  by  raising  the  lower  tone  a  small  half  step,  and  not 

by  lowering  the  upper,  is  clearly  to  be  seen  from  the  above  table  of  inver- 

N^ions.     Since  the  diminished  intervals  result  from  the  augmented  through 

the  inversion  in  the  octave,  this  formation  comes  of  itself;  for  example, 

if^nz  must  of  necessity  give  the  following  dim- 


the  augmented  fourth 


mished  fifth  :   /W— r,^ — 

jg — 


Just  so  the  perfect  fourth  belongs  originally  to  the  consonances,  since 


20  MANUAL    OF   HARMONY. 

by  inFersion  it  is  converted  into  the  perfect  fifth,  in  the  same  manner  aa 
the  perfect  fifth  can  only  produce  the  perfect  fourth,  and  never  in  any  case 
does  a  dissonance  result  from  the  inversion  of  a  consonance  in  the  octave. 
Mention  is  made  of  this  here  because,  in  particular  cases  which  are  men- 
tioned farther  on,  the  fourth  requires  a  similar  treatment  with  some 
dissonances,  which  induced  some  theorists  in  earlier  times,  to  explain  it 
simply  as  a  dissonance. 

It  will  likewise  be  clear  that  the  augmented  octave,  as  also  the  ninth, 
cannot  be  inverted,  since  they  never  can  become  intervals  below. 

Other  kinds  of  inversions,  such  as  those  in  the  tenth  and  twelfth,  which 
produce  entirely  different  results,  may  be  passed  over  here,  since  they  ex- 
ercise no  influence  upon  our  next  studies. 

Since  a  complete  and  certain  knowledge  of  all  intervals  is  indispensable 
for  the  following  harmonic  studies,  the  practice  of  them  in  writing,  as  als© 
an  oral  solution  of  given  intervals,  will  facilitate  much  their  correct  com- 
prehension,— which  exercises  are  to  be  repeatedly  employed. 


HARMONY. 


Combinations  of  simultaneous  tones,  formed  from  different  intervals, 
according  to  certain  fundamental  principles,  are  called  in  general,  Harmo' 
nieSf  Chords. 

The  doctrine  of  harmony  makes  us  acquainted  with  the  different  species 
and  kinds  of  chords,  and  shows  their  natural  treatment.  This  consists  in 
the  right  and  natural  connection  of  the  chords  among  themselves,  that  is, 
in  the  transition,  the  resolution,  the  commingling  of  one  chord  into  and 
with  the  following. 


I  PART     I. 

THE  FUNDAMENTAL  HARMONIES  AND  THE  CHORDS  DERIVED 

FROM  THEM. 

Among  the  various  kinds  of  chords  which  can  serve  for  the  harmonic 
foundation  of  a  composition,  those  which  present  themselves  as  indepen- 
dent, without  a  definite  connection  with  others,  can  be  easily  distinguished 
from  those  which  indicate  plainly  a  connection  with  other  chords,  and  are 
therefore  not  independent. 

To  the  first  belong  the  most  of  the  triads,  to  the  last  the  chords  of  the 
seventh.  These  two  kinds  form  the  fundamental  harmonies,  from  which 
all  remaining  chords  are  derived. 


CHAPTER    I. 

Tlie  Triads  of  the  3IaJor  Scale, 


A  triad  is  formed  by  a  combination  of  three  different  tones.  Of  these, 
the  lowest  is  called  fundamental  tone,  to  which  its  third  and  fifth  are 
^^dded,  e.  g. 


;£ 


22  MANUAL    OF   HARMONY. 

These  triads,  formed  upon  c,  g  and  a,  present,  however,  a  difference  as  tc 
their  intervals.  While  the  triads  of  c  and  g  are  formed  here  hj  majo7 
thirds  SLud  2>erfect  fifths  J  the  triad  of  a  contains  a  minor  third  and  perfect 
fifth.    ^ 

A  triad  with  major  third  and  j) erf ect  fifth  is  called  a 
MAJOR    TRIAD. 

A  triad  with  minor  third  and  perfect  fifth  a 
MIN^OR    TRIAD. 

Remark. — The  explanation  of  other  kinds  of  triads  cannot  follow  until  farther  on. 

As  the  diatonic  scale  makes  up  the  content  of  a  key,  and  forms  the 
foundation  of  the  melodic  successions,  so  also  the  triads,  which  are  founded 
upon  the  different  steps  of  the  scale,  will  form  the  essential  part  of  the 
harmonic  content. 

Natural  Connection  of  the  Triads  of  a  Key, 

The  triad  which  rests  upon  the  first  step  of  a  key,  is  indeed  the  most 
important,  the  one  which  determines  the  key ;  there  stand,  however,  others 
in  the  nearest  connQdiion  with  it,  which  make  clear  its  position. 

In  the  natural  presentation  of  the  triad  in  thirds,  the  lowest  tone  shows 
itself  as  fundamental,  the  ffth  as  highest  tone,  and  at  the  same  time  as 
its  culmination. 


Fundamental. 

Each  farther  addition  of  a  new  interval  would  either  alter  the  chord,  or 
present  tones  already  there,  doubled.  The  next  triad  standing  in  connec- 
tion with  this  must,  to  be  sure,  as  an  independent  chord,  lie  outside  its  tone- 
mass,  still,  however,  support  itself  upon  one  of  its  tones.  This  tone  can 
only  be  found  in  the  outer  limits  of  the  chord,  viz  :  in  c  and  g.  G,  which 
is  here  the  fifth,  will  thus  form  the  fundamental  of  the  one  nearest 
standing  triad,  while  c  will  in  the  same  manner  form  the  culmination,  the 
■fifth  of  the  other,  the  fundamental  of  which  would  be  F. 

The  connection  of  these  three  chords  can  be  most  plainly  presented  in 
the  following  manner : 


«>i?=i^^ 


It  is  especially  to  be  remarked  of  these  three  triads  which  stand  in  the 
closest  connection,  that  their  tones  contain  all  the  tones  of  the  scale ;  that 
they  form  the  fundamental  features  of  the  key,  and  that  they  are,  and  must 


MANUAL    OF   HARMON?. 


23 


be  those  most  frequently  employed  in  practice,  if  the  key  is  to  present 
itself  clear  and  distinct. 

On  account  of  their  importance  also,  especial  names  have  been  given  to 
them.  The  one  first  found,  standing  upon  the  first  degree  of  the  scale,  if 
called 

THE    TONIC     TRIAD. 
The  second,  upon  the  fifth  degree, 

THE    DOMINANT    TRIAD. 
The  third,  upon  the  fourth  degree, 

THE    SUB-DOMINANT    TRIAD. 
If  we  arrange  these  three  chords  according  to  their  order  in  the  scale, 
they  present  themselves  to  us  thus : 


t 


^ 


I  IV  V 

\  and  they  show  themselves  collectively,  as  major  triads. 

Application  of  the  Harmonies  I>iscovered, 

In  the  application  of  these  three,  as  well  as  of  later  chords,  we  avail 
ourselves  of  the  four-voiced  manner  of  writing. 

Remark. — The  theoretical  chord  combinatioo  can  be  well  presented,  to  be  sure,  three- 
voiced  in  manifold  relation.  It  would,  however,  detain  us  longer  from  our  practical 
aim,  and  may,  for  this  reason,  be  reserved  for  a  special  presentation.  The  four-voiced 
movement  will  always  maintain  its  importance  as  the  foimdation  of  all  kinds  of  com- 
position. ■ 

We  regard,  however,  each  harmony  not  as  a  mere  mass,  as  compositions 
for  the  piano-forte  often  present  them,  but  divide  its  component  parts  into 
four  different  voices. 

The  upper  is  called  Soprano,  the  lowest  Bass,  these  two  together  are 
called  the  outer  voices  :  the  voice  next  below  the  Soprano  is  called  Alto,  the 
one  next  above  the  Bass,  Tenor;  these  two  together  are  called  middle-voices. 

The  arrangement  of  these  voices  in  the  manner  of  a  score  is  as  follows, 
and  the  triad  may  be  exhibited  thus : 

5. 

80PKAN0. 


Alto. 


Tknor. 


Bass 


illpJllB 


24 


MANUAL    OF   HARMONY. 


For  the  upper  three  voices  especial  clefs  are  used,  which  conform  better 
to  their  compass  than  the  above  used  violin  [G]  clef,  and  which  will  be 
spoken  of  later. 

For  our  next  exercises,  we  select  for  the  sake  of  an  easier  view  of  the 
whole,  not  a  separate  staff  for  each  voice,  but  will  use  the  usual  form  of 
writing  for  the  piano,  (upon  two  staves). 

The  distribution  of  voices  in  No.  5,  may  be  exhibited  thus : 


6. 

Soprano, 

A  LTO. 

Tksor. 


Uass. 


m: 


m^mimm 


^^^^mm:^ 


A  twofold  consideration  of  these  various  voices  will  take  place  :  first  in 
relation  to  the  progression  of  each  voice  for  itself  alone,  then  in  its  relation 
to  the  remaining  voices,  both  of  which  must  be  pure  and  ivell-constructed. 

The  result  of  the  fulfillment  of  these  two  conditions  is  called  pure  lead- 
ing of  the  voices. 

This  purity  of  the  harmony  and  its  progression  is  attained  through 
•seeking  out  and  practicing  the  natural  and  legitimate  of  harmonic  com- 
bination. 

Hereby  arises  the  so-called  pure  harmonic  structure,  also  called  strict 
style,  which  prescribes  rules  and  laws  which  proceed  from  the  nature  of 
music  itself,  the  observance  of  which  will  afford  the  safest  foundation  for  a 
later  free  use  of  the  materials  for  composition.  By  exercises  in  the  pure 
harmonic  structure  is  the  judgment  sharpened,  the  sense  for  the  true 
and  correct  formed,  and  the  taste  purified. 


Remark. — Inasmuch  as  every  composition  should  exhibit  itself,  through  a  correct 
use  of  all  means  at  command  and  the  purity  resulting  therefrom,  (purity  is  here  synony- 
mous ■with  natural  expression),  the  term  pure  harmonic  structure  in  a  general  sense, 
■would  require  no  farther  explanation,  as  being  a  matter  of  course.  In  a  more  narrow 
sense,  Iwwever,  under  pure  harmonic  structure  "we  understand  something  farther,  ■which 
is  more  nearly  and  better  indicated  by  the  expression  of  like  meaning,  strict  harmonio 
structure,  strict  style,  since  this  can  be  used  in  distinction  to  free  style,  whereas,  properly 
Bpeaking,  no  antithesis  of  the  pure  structure,  such  as,  perhaps,  impure  structure,  is  to  be 
assumed,  since,  as  frequently  as  the  latter  in  fact  may  occur,  it  -were  certainly  to  be 
designated  as  false,  -while  the  free  structure  might  be  essentially  founded  upon  the  legiti- 
mate of  the  pure  structure. 

As  was  indicated  above,  by  pure  harmonic  structure  h  understood  in  a  narro-wer  senses 


MANUAL    OF   HARMONY. 


25 


inch  a  one  as  in  the  natural  development  of  all  tone  relations,  allows  the  fewest  digressions 
from  the  legitimate,  and  only  such  as  do  not  toicch  that  which  is  essential,  fundamental. 

If,  in  what  precedes,  the  idea  of  pure  harmonic  structure  is  determined  in  a  general 
way,  still  its  boundaries  are  not  yet  drawn ;  and  just  this  is  a  point  which  gives  rise  to  tl  e 
more  difficulties  for  the  beginner,  as  the  boundaries  are  so  very  variously  determined  by 
the  theorists  themselves.  This  difficulty  has  occasioned  many  of  them,  especially  some 
later  ones,  to  omit  entirely  to  speak  of  the  pure  construction,  of  the  strict  style ;  indeed, 
to  begin  immediately  with  composition,  and  teach  the  laws  of  harmony  from  its  inci- 
dents. Whether  this  indulgence  to  youthful  impatience,  which  does  not  willingly  busy 
itself  with  the  abstract,  this  inclination  towards  premature  living  creation,  before  the 
organic  has  developed  itself  to  the  capability  for  creation,  can  produce  anything  really 
mature,  need  not  be  further  investigated  here. 

Let  those  who  follow  the  views  of  this  book  and  conform  their  studies  to  them,  as 
also  all  who  have  to  go  through  a  strict  school,  be  assured,  that  their  freedom  for  future 
creation  will  by  no  means  be  lost  by  means  of  that  which  is  forbidden  to  them,  but 
will  unfold  itself  so  much  the  more  fully,  and  with  a  more  living  power,  upon  a  basis 
conformed  to  nature.  The  real  mastery  has  ever  been  able  to  make  itself  apparent 
most  genially  within  prescribed  bounds,  whereas  the  most  lawless  conceits  frequently 
furnish  proof  of  morbidity  and  weakness  of  mind.  On  the  other  hand,  the  pupil  cannot 
be  justified  in  making  use  of  exceptions  to  given  principles,  which  may  perhaps  be  found 
in  the  works  of  the  greatest  masters,  where  the  rule  is  concerned ;  or,  in  any  case,  to  wish 
to  produce  compositions,  when  the  thing  to  be  done  is  to  work  out  exercises  theoretically 
well. 

The   three  chords  thus   far  known,  being    applied  in  the  four-voiced 
movement,  will  give  occasion  for  remarks  and  observations,  from  which 
certain  fundamental  features  and  rules  are  to  be  established. 
/\    Since  the  triads  only  contain  three  tones,  one  component  part  (interval) 
tjiereof,  must  be  doubled,  if  they  are  to  be  used  in  four-voiced  writing. 


A 


Any  Interval  of  the  Triad  can  be  Doubled, 

The  fundamental^  however,  usually  presents  itself  as  the  tone  most 
adapted  for  doubling,  more  rarely  the  fifth  and  third,  and,  indeed,  the 
latter,  in  many  cases  which  will  be  shown  later,  is  not  to  be  doubled  at  all. 

In  order  to  accomplish  the  connection  of  two  triads,  the  following  rule 
is  to  be  observed : 

If  a  tone  occurs  in  both  of  two  chords  which  are  to  he  connected^  it  it 
to  he  retained  in  the  same  voice,  e.  g. 


V 


V 


y^- 


26 


MANUAL    OF    HARMONY, 


In  the  Example  a,  C  occurs  in  both  triads  as  common  tone  ;  the  Soprano, 
/  which  gave  the  first  C,  retains  it  also  as  fifth  of  the  next  chord.     Just  so 
/   in  Example  &,  in  which  the  Gr  of  the  Alto  affects  the  connection. 


The  remaining  voices  proceed  to  the  tones  which  lie  nearest  to  theniy  as 
a  the  Alto  from  Gr  to  A,  the  Tenor  from  E  to  F,  &c. 
5k  If  in  two  chords  no  common  tone  appears^  the  voices  are  independently 


\yj/Th 

Y^t  a  the  Alto  from  G  to  A,  the  Tenor  from  E  to  F,  &c. 
/^  If  in  two  chords  no  common  tone  appears,  the  voices  vuic,  v 
(^  led  in  such  a  manner/that  none  appears  with  any  other 


m  PARALLEL 


FIFTHS  or  OCTAVES. 

In  order  to  explain  this  faulty  progression  more  exactly,  we  must  first 
make  the  necessary  explanation  of  the  movement  of  the  voices  in  refer- 
ence to  each  other. 


The  Helation  of   tlie  3Iovement   of  the    Voices  in   Mespect  to 

each  other. 

One  voice  can  progress  with  another  in 

Parallel  [direct]  motion  (motus  rectus), 
Contrary  motion,  [motus  contrarius)  and 

Oblique  motion,  (motus  obliquus). 

The  parallel  motion  arises,  if  two  voices  rise  or  fall  at  the  same  time,  e.  g. 


ict 


1^1 


i 


2^zz=?: 


=:^i=izi:: 


:S ^: 


They  progress  in  contrary  motion  if  the  one  rises  and  the  other  falls,  e.  g. 


•   "^ 


p    •* 


I    =>'  -J     I 


7 


The  oblique  motion  arises,  if,  of  two  voices  one  remains  upon  the  same^ 
tone  yhile  the  other  moves  on,  e.  g. 


MANUAL    OF   HARMONY, 


27 


These  three  kinds  of  movement  of  the  voices  occur  in  chord  connections 
niB,mixed  manner.  Thus,  in  Example  No.  7,  b,  the  parallel  motion  shows 
itself  between  Soprano  and  Tenor,  the  contrary  motion  between  Soprano, 
Tenor  and  Bass,  and  the  oblique  motion  between  the  Alto  and  the  remain- 
ing voices. 

The  above  mentioned  faulty  movement  of  the  voices  in  parallel  octaves 
and  fifths^  can  only  appear  in  parallel  motion  :  if,  for  example,  two 
voices  progress  by  degrees  or  skips  in  the  following  manner : 


11. 


This  fault  is  regarded  as  such  for  all  voices. 

The  following  connections  of  harmony  contain  both  faults : 


12. 


h. 


In  Example  a,  are  parallel  octave  skips  between  Soprano  and  Bass;  in 
Example  &_,  octave  progressions  between  Alto  and  Bass,  and  in  Example  c^ 
between  Tenor  and  Bass.  Parallel  fifths  are  to  be  found  in  q^  between  Alto 
and  Bass ;  in  &,  between  Tenor  and  Bass,  and  in  c^  between  Soprano  and 
Tenor,  as  also  at  the  same  time  between  Soprano  and  Bass. 

The  best  means,  to  avoid  these  and  similar  faulty  progressions,  is,  for 
the  above  cases,  the  use  of  the  contrary  and  ohlique  movement  of  the 
voices ;  that  is,  the  voice  which  already  forms  an  octave  or  fifth  with 
another,  must  either  move  with  it  in  contrary  motion^  or,  if  the  following 
chord  contains  the  same  tone,  remain  stationary.  The  other  voices  then 
move  on  to  the  tones  of  the  new  harmony  which  lie  nearest  to  them. 

Thus  in  Example  12,  d  the  oblique  motion  in  respect  to  one  voice,  and  at 
J)  and  Cf  the  contrary  motion  of  all  voices  in  respect  to  t.he  Bass,  is  to  be 
applied,  e.  g. 


13. 


^^^M\ 


"W 


lilii[^ 


28  MANUAL    OF   HARMONY. 

Remark. — ^The  reason  for  the  prohibition  of  octaves^  with  whi<5h  is  connected  that  oi 
the  progression  in  unison,  can  be  easily  found  in  the  necessary  independence  of  the  voices. 
It  is  more  difficult  to  discover  the  ground  for  the  prohibition  of  the  progression  in  fifths, 
strong  as  the  conviction  may  be  of  the  necessity  of  it ;  and  from  the  earliest  times  until 
no-w,  much  pains  has  been  taken  to  express  it  clearly  and  definitely.  On  this  point,  let 
tlie  following  view  be  examined. 

If  each  chord-formation  presents  for  itself  a  separate  whole,  which,  let  it  be  formed 
as  it  may  in  other  respects,  is  bounded  mainly,  as  it  were,  by  its  fundamental  and  the 
fifth,  as  by  a  circle,  (the  seventh,  as  something  additional  cannot  here  be  taken  into 
account),  and  if  the  connections  of  harmony  can  only  be  produced  by  this :  that  one 
chord,  so  to  speak,  goes  over  into  and  resolves  itself  into  the  other ;  then  it  is  evident, 
that  two  chords  with  their  boundaries,  fifth  after  fifth,  do  not  resolve  themselves  into 
each  other,  but,  if  they  are  placed  side  by  side,  will  appear  without  relation  to  each 
other.    This  can  be  observed  if  we  compare  the  following  examples  : 


14.    ©5S=i^..       .     _^_^ 


M^^i^mw^i 


The  sevenths,  however,  neither  form,  properly,  new  chords,  nor  do  they  lie,  (according 
to  the  idea  of  a  seventh),  outside  of  the  circle  of  the  original  chord,  and  only  serve  to  indi- 
cate the  relations  of  two  chords,  and  to  make  the  connections  of  the  harmonies  more 
intimate  and  firmer. 

Everywhere  now,  where  the  perfect  fifth  appears,  it  will  carry  in  itself  its  character 
of  boundary/ ;  the  remaining  constituents  of  the  chord,  (as  it  were  the  content  of  the 
fifth),  or  anything  additional,  as  the  seventh,  may  lie  above  or  below  it ;  the  unpleasant- 
ness of  the  succession  of  two  perfect  fifths  will  always  be  discoverable  in  the  deficiency 
in  connection. 

Since  we  have  spoken  here  of  the  fifths  of  the  triads  only,  it  may  still  be  remarked, 
that  in  the  case  of  perfect  fifths  which  arise  from  added  sevenths,  the  rule  of  their  pre- 
paration, in  part,  to  be  sure,  prevents  parallel  fifths,  of  itself;  that,  however,  in  the 
progression  of  one  such  seventh,  which  forms  a  perfect  fifth  with  another  voice,  to  a 
following  perfect  fifth,  this  last  will  cause  the  unpleasantness  and  deficiency  of  the 
connection  to  be  heard,  since  this  lies  only  in  the  second  fifth,  which  enters  without  con- 
nection, €.  g. 


15. 


As  eoncems  the  diminished  fifth,  however,  which  in  the  dominant  chord  of  the 
seventh  can  enter  free  under  certain  conditions,  its  free  entrance  even  in  the  case  of  par- 
allels, justifies  completely  the  above  expressed  view,  since,  so  soon  as  it  appears  after 
the  perfect  fifth,  its  connecting  character  makes  itself  felt,  whereas,  before  the  perfect 


MANUAL    OF   HARMONY. 


29 


fifth,  leaving  out  of  the  account  its  farther  laws  of  progression,  the  latter  immediately 
gteps  outside  of  the  circle  of  connection  of  both  harmonies. 
Compare  the  following  examples, 


16. 


If,  however,  instances  of  the  following  sort  are  frequently  found  in  compositions  of 
the  stricter  style  : 


IT. 


we  may  assume  that  the  doubling  of  the  diminished  fifth  (the  /,)  requires  a  double  pro- 
gression of  the  same,  and  that  the  fifth-succession  is  thereby  justified,  because  it  lies  Id 
the  middle  voices ;  that,  however,  the  following  progression  could  not  be  called  pure, 


IS. 


--J- 


2L^ 


I 


a^^^P^^^^^s^ii 


partly  because  they  come  forward  too  prominently  in  the  upper  voice ;  partly  because 
the  above  condition  of  the  necessary  double  progression  is  wanting,  although  instances 
such  as  No.  16.  c,  are  often  to  be  heard. 

Hereby  it  becomes  clear,  also,  why  such  parallel  fifths  as  arise  from  passing  notes, 
in  many  cases  do  not  sound  so  unpleasant  as  those  spoken  of  above,  for  which  reason 
many  theorists  recognize  them  as  faultless ;  which,  at  any  rate,  cannot  be  unconditionally 
admitted,  since  many  of  them  are  based  upon  other  false  voice-progressions,  (for  exam- 
ple, upon  covered  fifths),  and  it  is  not  to  be  denied,  that  with  a  very  open  position  and 
sufficient  duration  of  the  same,  the  unpleasantness  of  their  operation  becomes  per- 
ceptible. 

It  is  not  the  place  here,  to  treat  at  greater  length  of  these  relations,  and  there  would 
be  much  to  say  on  many  points  ;  as  for  example,  concerning  the  progression  of  the  fifth 
of  the  augmented  chord  of  the  sixth  and  fifth,  which  would  here  carry  us  too  far. 
Individual  casea  will  bring  us  back  to  this  T^mi  in  connection  with  our  practical 
exercises. 


so 


MANUAL    OF   HARMONY. 


If  the  sense  of  the  foregoing  representation  should  still  be  too  obscure  to  the  begin- 
ner, yet  with  more  advanced  knowledge,  and  exercises,  and  necessary  frequent  repetitions 
of  the  entire  harmonic  system,  the  comprehension  of  it  will  not  long  be  wanting. 

The  faulty  progression,  thus  far  mentioned,  is  called  open  fifth  and 
octave  progression. 

They  are  covered^  if,  in  parallel  motion  of  two  voices,  the  second  interval 
forms  2i- fifth  or  octave^  e.  g. 


19. 


Open  fifth  and  octave  parallels  remain,  for  harmonic  combinations 
always  inadmissible ;  the  worth  of  covered  fifths  and  octaves  will  be  dis- 
cussed farther  on  (in  Chapter  XVII.) ;  for  the  present,  this  matter  must 
be  left  to  oral  instruction,  since,  in  general,  with  a  correct  comprehension 
of  the  exercises,  not  much  opportunity  will  be  offered  for  making  unsuit- 
able fifths  and  octaves. 

Hemark. — The  beginner  will  do  well,  in  working  out  the  first  examples,  to  leave 
covered  fifths  and  octaves  entirely  unnoticed,  since,  in  a  too  anxious  avoidance  of 
them,  frequently  the  first  principles  of  chord-connection  are  violated,  and  other  much 
worse  faults  easily  arise.  Much  which  follows  will  lead  us  back  to  this  point,  and  with 
a  more  mature  insight,  the  subject  will  be  particularly  discussed. 

Exercises, 

To   bring  musically   into   connection  the   three   primary   triads,  with 
observance  of  the  rules  thus  far  established,  will  be  the  next  exercise. 
We  select  for  this  purpose  the  following  Bass  progression : 


20. 


§3 


;i^i 


IH^i 


C:   I 


IV 


P 


i 


Remark. — ^Tliese,  as  well  as  all  subsequent  exercises,  give  an  indication  in  what  way 
and  manner  our  practical  exercises  will  proceed.  They  are  always  to  be  continued  so 
long  as  the  point  under  consideration  makes  it  necessary. 

The  situation  of  the  upper  three  voices  of  the  first  chord,  which  arc  to 
be  added,  will  yet  give  us  occasion  for  important  remarks. 

*  The  figure  over  the  Bass-note  indicates  the  proper,  interval  for  the  Soprano  of  the 
first  chord. — Ed. 


ZfANUAL    OF    HARMONY. 


31 


¥ 


We  Iiave  already  seen  in  Example  5,  that  the  situation  of  the  voices  in  a 
chord  can  be  very  different.  This  situation  of  the  voices  is  called  the 
'position  of  the  chord. 

Close  and  Open  Position, 


A  chord  appears  in  close  position,  if  the  upper  three  voices  lie  so  near 
to  each  other   that  neither  the  Soprano  nor  Tenor,  if  transposed  an  octave, 
can  appear  between  the  two  other  voices,  even  if  the  Bass  is  somewhat 
^_  removed,  e.  g. 


21. 


<7. 


The  first  position  of  the  chord  a  is  in  &  so  altered,  that  the  former  E  of 
the  Tenor  being  placed  an  octave  higher  is  given  to  the  Soprano ;  in  c,  the 
case  is  the  same,  with  the  two  tones  Gr  and  E ;  on  the'  other  hand,  in  d^  the 
C  of  the  Soprano  is  placed  an  octave  lower.  In  all  these  transpositions 
the  situation  is  indeed  altered,  but  not  the  close  position. 

It  is  otherwise  if  the  chord  appears  in  o'pen  (also  called  dispersed)  posi- 
tion, which  is  the  case  if  either  the  Soprano  can  be  placed  between  the 
Alto  and  Tenor,  or  the  Tenor  between  Alto  and  Soprano,  so  that  thereby 
the  close  position  results,  e.  g. 


22. 


At  cif  the  chord  appears  in  open  position ;  by  a  transposition  of  the  G 
between  the  Alto  and  Soprano  in  close  position  &/  just  so  at  c  and  d.  At  /' 
the  G  of  the  Soprano  of  the  chord  e^  is  placed  an  octave  lower  between  the 
Alto  and  Tenor. 

In  this  sense,  however,  the  following  situation  of  the  voices  (No.  23), 
would  not  be  open  position,  for  by  the  transposition  of  the  Tenor,  the 
situation  of  the  upper  voices  would   not  be  altered,  hf  and   only  the 


32 


MANUAL    OF   HARMONY. 


transposition  of  the  Soprano  would  produce  the  real  open  position  of  the 
chord,  c» 


23.  ; 


1 


^=&=\^^l=^=\l 


Even  if  the  open  position  allows  the  chord  to  appear  fuller,  still  it  ia 
not  always  to  be  applied,  and,  for  our  first  exercises,  is  not  clear  enough  to 
the  view ;  so  that  we  will  for  the  present,  write  them  in  close  position. 

Remark. — It  will  always  be  better  in  the  beginning  to  work  out  the  examples  in 
close  position,  and  only  to  use  the  open  position  later,  from  the  examples  of  the  second 
and  third  part  onward,  in  which  last  they  necessarily  present  themselves.  In  the  begin- 
ning, the  pupil,  in  the  use  of  the  open  position,  stumbles  now  and  then  upon  difficulties,  to 
overcome  which  cannot  be  our  immediate  object,  and  which  had  therefore  better  be 
evaded. 

The  various  positions  do  not  generally  appear  single,  but  occur  com- 
bined, according  as  the  leading  of  the  voices  requires. 

If  the  position  of  the  first  chord  is  determined,  the  following  chords  are 
no  longer  so  free,  as  to  their  position,  that  each  can  be  chosen  at  pleasure, 
but  it  is  regulated  according  to  the  rules  for  the  connection  of  chords 
already  given,  pages  25  and  26. 

This  connection  of  chords  and  the  leading  of  the  voices  of  the  first 
exercise,  No.  20,  may  follow  thus : 


24. 


=^^i^§liiE 


g!=5E 


iz^: 


C:'  I 


:  :~ffl~: : 


IV 


The  natural  relation  of  these  chords  to  one  another  becomes  clear  by 
the  above  simple  example,  if  we  observe  accurately  their  connection ; 
especially,  however,  from  the  last  two  chords  does  the  close  connection, 
the  mutual  completing  of  one  another,  become  plain.  The  feeling  of 
return,  of  rest,  of  satisfaction,  which  lies  in  this  connection  of  chords, 
adapts  them  for  forming  the  close.  This  form  of  close  through  the  domi- 
nant chord,  which  resolved  itself  into  the  tonic  triad,  is  called,  if  the  latter 
falls  upon  the  rythmical  accent,  the  authentic  close.     [Cadence]. 


MANUAL    OF    HARMONY. 


3d 


35. 


Another  form  of  close,  which  is  formed  by  the  subdominant  triad,  aa 
above,  No.  20,  Example  4,  is  called  the  pJagal  close. 


36. 


1 


i^il^i 


IV  I 

Of  these  and  other  kinds  of  close,  we  cannot  speak  more  at  length,  until 
later. 

In  order  to  become  expert  in  writing  the  succession  of  chords  which 
occurs  if  the  Bass  progresses  by  degrees,  (as  in  Example  24,  F — Gr),  it  will 
be  to  the  purpose  to  write  the  successions  IV-Y  and  Y-IY,  in  various 
positions  and  keys. 

Note. — The  expression  hy  degrees  is  used  here,  as  elsewhere  in  similar  connection,  to 
denote  from  one  degree  to  the  next,  in  distinction  to  hy  ships,  viz.,  from  one  degree  t*. 
another  at  a  greater  distance. — Ed. 


The  Triads  of  the  Remaining  Degrees  of  the  Major  Scale, 

All  triads  of  the  remaining  degrees  of  a  scale  will,  to  be  sure,  belong 
to  one  and  the  same  key,  but  will  not  indicate  it  so  decisively  as,  for  exam- 
ple, the  combination  of  chords  V-I. 

These  triads  are  called,  to  distinguish  them  from  the  primary  triads, 

SECONDARY    TRIADS. 

They  are  situated  upon  the  second,  third,  sixth,  and  seventh  degrees  of 
the  scale. 


27 


■I 


:r=^ 


A. 


_iLX 


vuo 


The   triads  of   the  second,  third,  and  sixth  degrees,  appear  as  minot 
triads,  since  their  thirds  are  minor  and  ihoii  fifths  perfect. 

The  triad  of  the  seventh  degree  is  materially  different  from  the  others* 


84  MANUAL    OF   HARMONY. 

because  that,  beside  the  minor  third,  it  contains  a  diminished  fifth  ;  for 
this  reason  it  is  called  the 

DIMINISHED   TRIAD. 

We  select  as  an  easy  distinguishing  sign,  for  the  minor  triad,  a  small 
numeral  for  the  designation  of  the  degree  upon  which  it  is  situated,  to 
which,  in  the  case  of  the  diminished  triad,  we  add  a  0,  as  above  vii°,  a 
manner  of  writing  which  the  theorist,  Gr.  Weber,  has  introduced. 

All  the  triads  of  the  major  scale  can  now  be  exhibited  thus  :  a 

^-f-i— i— =-=^ —     (R^n 

I  n         ni       IV        V        VI       viio  ^ 

Remark. — The  beginner  must  be  very  careful  not  to  conceive  of  these  chords,  at  their 
appearance,  as  all  tonic  triads,  a  misunderstanding  -which  renders  insight  into  harmonic 
combinations  much  more  difficult.  As  long  as  C  major  is  the  ruling  key,  the  triads  of 
G,  F,  D,  etc.,  are  nothing  else  than  the  chords  of  the  various  degrees  of  this  Jcey  of  0 
major,  and  belonging  to  it,  and  no  mention  will  be  made  of  G  major,  F  major,  d  minor, 
so  long  as  these  keys  do  not  appear  as  independent. 

Hereby  arises  an  ambiguity  of  the  chords,  which  should  be  particularly  noticed 
Each  triad  can  belong  to  various  keys.    The  major  triad  of  C  can  be : 


29. 


HiEl^^ii 


C:    I  F:    V  G:    IV 


If,  therefore,  in  respect  to  this  chord,  C  major  is  spoken  of  (expressing  the  key  m  the 
general  use  of  language),  this  is  true  only  in  the  first  case,  if  the  C  major  triad  occu- 
pies the  frst  degree  ;  in  all  other  cases,  however,  it  is  incorrect. 

Application, 

In  the  connection  of  these  chords,  as  well  among  themselves  as  also  with 
those  found  before,  no  new  rule  is  at  present  necessary.  Several  things 
v^hich  are  new  will,  however,  appear  in  connection  with  it. 

The  Bass  can  move  either  by  skips  or  hj/  degrees.* 
/  In  the  first  case  there  will  always  be  connecting  tones  (like  tones  in  two 
/consecutive  chords) ;  in  the  last  the  progression  of  the  voices  must  be  in 
j  contrary  motion,  according  to  a  rule  mentioned  above,  (page  26),  in  order 
to  bring  out  the  inner  connection  of  the  chords. 

•  See  Translator's  note  on  page  83. 


MANUAL    OF    HARMONY. 
a.     The  Bass  progresses  hy  skips. 

b.    NB. 


35 


better: 


30. 


• — '^f^^i — ^"        1 — g-  -        — g- — g—         p 


u       IV 


:gfF=S: 


gll 


9^ 


i 


II  VI  &c. 

As  in  this  example,  the  skips  in  the  Bass  from  the  second  degree  have 
been  treated,  the  same  can  be  treated  beginning  from  all  other  degrees,  so 
that  tones  common  to  the  tico  chords  always  remain  in  the  same  voice. 

To  this  rule  there  are,  however,  in  many  cases,  exceptions. 

In  Example  30,  at  NB.,  is  found  a  progression  of  the  voices  formed 
according  to  the  above  rule,  which  contains  an  unpleasant  covered  octave 
between  Tenor  and  Bass,  and  which  is  certainly  improved  by  the  following 
progression.  Even  if,  in  the  last  case,  the  local  connection  of  the  tones 
fails,  still  the  inner  connection  is  present,  since  the  D  of  the  Soprano  in 
the  first  chord  can  easily  be  conceived  as  doubled  through  the  lower  octave, 
whereby  the  connection  immediately  becomes  apparent,  as  in  Example 
No.  31 : 


31. 


^m 


r^ 


Remaek. — The  reason,  however,  why  exactly  this  tone  should  be  conceived  as  double, 
since  this  could  also  be  the  case  with  any  tone  at  pleasure,  is  founded  upon  the  fact  that 
it  is  WxQ  fundamental^  the  tone  which  gives  to  the  whole  chord  its  determination. 

The  unpleasantness  of  the  covered  octave  mentioned,  lies  in  the  circum- 
stance, that  the  upper  voice  progresses  a  whole  step,  and  is  yet  more 
noticeable  if  it  is  contained  in  the  outer  voices,  as  in  Example  32  at  a* 


32. 


:miii 


36 


MANUAL    OF   HARMONY. 


By  the  contrary  motion  of  the  Bass  at  h,  the  leading  of  the  voices 
can  be  improved ;  in  like  manner,  by  the  contrary  motion  in  Example  c, 
although  here  also  a  covered  fifth  shows  itself  between  Soprano  and  Tenor. 
(See  the  Remark  on  Example  34). 

Remakk. — Id  the  cases  brought  forward  above,  we  do  not  speak  of  absolute  faults. 
If  the  leading  of  the  voices  is  entirely  given  into  our  control,  much  can  be  avoided, 
which  under  other  circumstances,  for  example,  in  the  treatment  of  a  cantu8  jirmus,  of  a 
motive,  or  on  other  grounds  important  for  the  composition,  is  unavoidable.  The 
improvement  is  here  only  presented  from  a  theoretical  stand-point.  Concerning  the 
covered  fifth  in  No.  32  c,  a  farther  explanation  follows  at  No.  34. 

/^^The  unpleasantness  of  the  covered  octaves  spoken  of  ceases  at  once  if 
the  njpper  voice  progresses  a  half  step,  e.  g. 


-k^- 


33. 


-JSrZ. 


M^^m^ll 


^iilHl 


i 


h.     The  Bass  progresses  hy  degrees. 
Here  the  contrary  motion  should  always  be  applied,  e.  g. 


NB.  1. 


lititer : 


31. 


lEig^i^lii^iiii 


g!^EE|EgE| 


-G 


l^gzi^-azj^gzzjzigzjngzzi^ 


titter : 


better  : 


m^mm^m=^^^m^- 


NB. 


:S^ 


gi^^Eg^^^l^i^^^-pg^^l^ 


ly 


IV 


|=E^ 


^h= 


m=Mm 


m 


-.zi^zz 


1 


IV 


MANUAL    OF    HARMONY, 


37 


HemarJcs  on  these  CJiord-contiections, 

In  all  progressions  of  voices  such  as  that  used  at  NB.  1,  and  subsequent 
similar  places,  it  is  better  to  double  the  third  of  the  second  chord,  in  order 
to  avoid  covered  fifths.  Their  unpleasantness  is  more  noticeable  if  the 
chords  appear  in  open  position,  e.  g. 


35. 


^i^i^^Ei^i; 


ifc 


i 


^mMi^^m 


-^- 


i 


The  leading  of  the  voices  at  h  is  to  be  preferred. 

If  these  covered  fifths  occur  in  the  middle  voices,  they  are  more  allow- 
able, because  they  are  less  perceptible. 


36. 


I^^fl 


zr  ^^.a 


m^m^ 


At  NB.  2,  the  doubling  of  the  third  of  the  second  chord  is  not  always 
to  be  applied,  since  in  general,  the  doubling  of  the  seventh  degree  (in 
Example  34,  the  B  of  the  second  chord),  is  to  be  avoided. 

Concerning  the  treatment  of  this  tone,  which  is  called  leading  ione^  a 
fuller  discussion  will  be  given  in  connection  with  the  following  exercises : 

Exercises  to  he  Worked  Out. 


87.   9ii^zz:s^=^g. 


EEEEi 


X 


m 


-« — fsiz:: 


^?Et  a 


§J=gn-= 


:e=£ 


\^E^JEx^i^=fZ 


-d <9- 


NB. 


5.^ 


wMw^^m^^^^^ 


The  fourth  exercise  gives  occasion  for  a  few  remarks. 

The  progression  of  the  Bass  takes  place  here  in  the  first  four  measures, 
in  a  regular,  consequent  manner.  Such  a  regular  harmonic  or  melodic 
progression  is  called  Sequence. 


38 


MANUAL    OF   HARMONY. 


This  consequent  progression  of  the  Bass,  occasions  also  a  like  regular 
leading  of  the  remaining  voices. 

The  treatment  of  this  example,  according  to  principles  of  chord-con- 
Dection  laid  down  above,  by  sustained  tones,  e.  g.j 


3§. 


-l-X 


--i=:|- 


wm 


i^ii^ii 


would  not  admit  of  the  attainment  of  this  end ;  the  progression  must 
rather  follow  in  such  a  manner,  that  the  chord  of  the  second  measure  is 
brought  into  the  same  position  which  that  of  the  first  measure  occupied, 
whereby  the  connecting  tone  D,  does  not  remain  in  the  same  voice. 


NB. 


Ill    vii*^ 


,  In  the  first  example,  on  account  of  the  sequence,  the  covered  octaves 

^        spoken   of  above   will   likewise  be  allowable,   if  they  are   not  found  in* 
outer  voices. 

In  the  third  measure  of  Exercise   No.  4,  we  meet  with  a  chord,  which 
thus  far  we  have  not  used. 


The  Diminished  THad. 

It  rests  upon  the  seventh  degree  of  the  major  scale,  and  is  more  depen- 
dent than  the  triads  found  thus  far,  since  it  plainly  indicates  a  progression, 
which  indication  is  effected  by  the  dissonance,  the  diminished  fifth. 

The  natural  progression  of  the  diminished  intervals  can  in  general  be  so 
conceived,  that  either  both  tones  approach  each  other  by  a  degree,  (a),  or 
the  upper  or  lower  tone  progresses  alone  over  against  the  other,  (ft,  c), 
a  kind  of  progression  which  only  becomes  plain  through  actual  chord-con- 
nection. 


40. 


Inversion. 


:if 


MANUAL    OF    HARMONY.  39 

The  third  following  the  diminished  triad  (rZ),  exhibits  the  triad  of  the 
first  degree  (C)  as  incomplete,  by  omission  of  the  fifth. 

Since,  according  to  the  relations  of  the  intervals  in  respect  to  inversion 
before  explained,  (page  18,  19,)  an  augmented  fourth  results  from  the  dimin- 
ished fifth,  its  progression  must  also  appear  in  inverted  order.     See  40  €, 

The  fundamental  tone  upon  which  the  diminished  triad  rests,  is  called 

LEADING    TOlN^E. 

It  is  found  again  as  third  in  the  dominant  triad,  and  as  fifth  in  the  triad 
of  the  third  degree. 


41.  fe— JE^^^^pzi-JJizifp 


VIlO 

Since  the  leading  tone  of  itself  comes  out  very  distinctly ,  it  is  not 
DOUBLED  in  the  simply  harmonic  four-voiced  movement. 

Just  so  its  progression  one  half  step  upwards  can  be  effected,  if  the 
next  following  chord  contains  this  tone. 

This  tendency  to  progression  lies  in  the  melodic  character  of  the  leading 

tone,  inasmuch  as  it  stands  as  half-step  before  the   fundamental  tone  of 

tie  scale.      This  is  noticeable  particularly  in  the  case  of  the  dominant 

'-ftpad,  if  the  leading  tone  is  contained  in  the  upper  voice,  as  a  in  Example 

42,  operates  more  satisfyingly,  than  b  and  c, 

d.-  e. 


§±e:s^^§^ 


^ 


'^^^ 


m 


m^ 


This  inclination  upwards  shows  itself  less  in  the  middle  voices,  as  at  d* 
Most  intolerable  in  many  cases,  in  such  chord-connections,  are  skips  in  tho 
upper  voice  (at  c),  whereas,  on  the  contrary,  skips  in  the  middle  voices 
(at  e)  are  to  be  used,  if  the  Bass  is  led  in  contrary  motion. 

In  Example  39,  third  measure,  is  found  a  doubling  and  progression  of 
the  leading  tone,  contrary  to  the  above  rule.  Both  took  place  on  account 
of  the  sequence  contained  in  the  example,  which  allowed  no  alteration  of 
the  position  or  the  progression  of  the  chord. 


Concerning  more  Extended  FormcUion  of  the  Close. 

The  formation  of  the  close  through  the  chord  of  the  dominant,  noticed 
on  page  32,  (the  authentic  close),  shows  itself  in  a  still  more  definite  man- 
ner in  the  last  examples. 


40 


MANUAL    OF    HARMONY. 


As  the  natural  relation  of  the  chord  of  the  dominant  to  the  tonic  triad, 
renders  the  two  adapted  to  the  formation  of  the  close,  so  in  these  ex- 
amples a  still  farther  preparation  of  it  is  noticeable,  through  the  triad  of 
the  second  degree,  which  stands  in  the  same  relation  to  the  chord  of  the 
dominant,  in  which  the  latter  stands  to  the  tonic  triad,  e.  g. 


43. 


yii 


1: 


h^-t-^ 


-I 1 — 


w 


Besides  the  triad  of  the  second  degree,  the  triad  of  the  sub-dominant  is 
also  adapted  for  this  formation  of  the  close,  e.  g. 


^iiiiHI 


44. 


^^mm^ 


IV 


The  closing  formulce  {cadences)  produced  by  this  chord-connection, 
will  assume  more  definite  form  through  the  application  of  the  chords  to  be 
shown  later. 


CHAPTER    II 


Tlie  Triads  of  the  Minor  Scale, 

a.     Primary  Triads. 

The  primary  triads  of  the  major  scale  were  found  upon  the  Jirst,  fourth 
Si-nd  fifth  degrees.  Upon  the  same  degrees  we  find  also  the  primary  triads 
of  the  minor  scale. 

The  relation,  however,  in  which  the  dominant  triad  stands  to  the  tonic 
chord,  that  is,  as  it  becomes  plain  through  the  formation  of  the  close  pre- 
viously shown,  renders  the  chromatic  alteration  of  one  tone  of  the  minor 
Bcale  necessary. 

Its  seventh  tone-degree,  which,  according  to  the  signature  of  the  minor 
scale,  is  always  distant  a  whole  step  from  the  eighth  degree,  is  chromati- 
cally raised  a  half-step,  so  that  it  acq^uires  the  character  of  a  leading 
tone,  e.  g. 


manvaL  of  harmony. 


41 


-_s: 


i 


45. 


By  this  means  the  formation  of  the  dominant  triad  in  minor,  becomes 
exactly  like  that  in  major,  thus  : 


A  minor. 


46. 


a 


A  major. 


*^  a:    V  A:    V 


or  briefly  expressed : 

The  dominant  triad  in  major  and  minor  is  always  a  major  triad. 
A  comparison  of  the  form  of  close  of  both  modes  shows  this  plainly : 


C  major. 


C  minor. 


47. 


lElEmiEfedbl^l 


'- G_i 


E^^^ 


That,  however,  the  sixth  degree  of  the  minor  scale  is  not,  in  a  harmonic 
sense,  capable  of  any  such  chromatic  alteration  by  elevation  a  half-step,  as 
is  often  necessary  melodically,  the  plagal  close  proves  a  (see  page  33), 
which  cannot  be  conceived  of  at  all  as  at  b» 


III  A  minor. 


h. 


4§. 


fe^ii=yEbld=i=lEi^lEiEii^ 


$i=t=M2=t^g:— t=|-±z:_^:zzt=:fe._._^. 


-fi? 


l^m 


=11^1=11 


The  three  primary  triads  in  minor  can  be  thus  exhibited  in  their  natural 
relation  according  to  previous  explanation  : 


49.    ^== 


=iNi= 


IV  I 


42 


MANUAL    OF   HARMONY. 


The  minor  scale,  as  it  forms  the  basis  for  the  formation  of  harmonies 


will  therefore  be  the  following  : 


50 


.ii 


I?: 


Remark. — All  other  forms  of  the  minor  scale,  such  as : 


51. 

or  descending : 

52. 


:M^ 


I 


-^g— ij^ 


depend  upon  melodic  conditions,  which  do  not  allow  the  step  of  an  augmented  second 
from  the  sixth  to  the  seventh  degree,  found  in  N"o.  50. 

These  forms  have  no  influence  upon  the  harmonic  formation  in  itself  considered  ;  the 
harmonic  foundation,  however,  has  a  reflex  influence  upon  the  minor  scale  itself,  as  the 
following  examples  show : 


53. 


E^5^i*i 


"*"  J  I        V  &c. 


*_^f.^l,< 


US 


The  last  case,  in  which  the  descending  scale  even  exhibits  the  step  of  an  augmented 
second  B-A  b,  which  in  future,  in  chord-connections  we  shall  carefully  avoid,  explains 
itself  thereby,  that  B  was  necessary  as  component  part  of  the  chord,  A|y,  however,  in 
order  not  to  destroy  the  minor  character  of  the  passage,  which  is  done  very  perceptibly 
through  A,  while,  in  the  ascending  scale,  (in  the  first  example),  this  (minor  character)  is 
already  perfectly  secured  through  the  minor  third,  Eb. 

b.     The  Triads  of  the  Remaining  Degrees  of  the  Minor  Scale. 
SECONDARY    TRIADS. 
After  the  establishment  of  the  minor  scale,  the  secondary  triads  appear 
in  the  following  form : 


54. 


Pi 


iio       ND. 


VI 


vuo 


MANUAL    OF    HARMONY,  43 

The   second   degree  gives   a   diminished  triad,  as  before,  the  seventh 
degree  of  the  major  scale ;  in  like  manner  a  diminished  triad  is  found 
upon  the  seventh  degree.     The  sixth  degree  forms  here  a  major  triad. 
^    The  third  degree  exhibits  a  new  form  of  the  triad. 

It  contains  a  major  third  and  an  augmented  fifth,  and  is  therefore  called 

THE    AUGMENTED    TRIAD. 

The  constrained  or  forced  character  of  the  connection  of  this  chord  with 
other  chords  of  the  same  key,  allows  it  seldom  to  appear  as  fundamental 
harmony  of  the  third  degree  of  the  minor  scale.  The  following  examples 
may  serve  to  prove  this  : 

a.  h.  c.  d.  e.  f. 


55. 


%l-^^irS^r2^irF^^I=r^%-^E^ 


77 
6  ^ 


(^^E^^^^^^^^^^ 


iio  IV  V  VI  viio 


Of  these  examples,  those  under  c  and  e  will  be  best  adapted  for  use. 
The  introduction  of  this  chord  shows  itself  to  be  more  difficult  still. 


d. 


56. 


6  6  6 

I  nO  IV  ^  V  YI 

Its  introduction  is  most  tolerable,  if  the  augmented  fifth  ia  prepared, 
that  is,  exists  already  in  the  same  voice  as  constituent  part  of  the  preced- 
ing chord,  (at  d). 

Remark. — There  is  something  peculiarly  foreign  in  the  chord  of  the  third  degree,  aa 
well  of  the  major  as  of  the  minor  scale,  so  that  this  harmony,  even  when  it  appears 
simply  as  minor  triad  in  the  major  scale,  is  very  difficult  to  connect  naturallr-  and  effec- 
tively with  other  chords,  and  therefore  seldom  occurs. 

Most  of  the  practicable  chord-connections  exhibited  above  will  occur  in 
other  relations,  and  not  allow  the  augmented  triad  to  be  recognized  as 
[triad  of  the]  third  degree  of  the  minor  scale.  The  augmented  triad, 
»vhich  is  much  used  in  the  later  music,  belongs  to  the  chromatically 
altered  harmonies,  which  will  be  explained  later  under  the  name  Altered 
Chords.     (See  Chap.  X,  Altered  Chords). 


44 


MANUAL    OF   HARMONY. 


Application, 

The  principles  of  the  connection  of  harmonies  and  leading  of  the 
voices,  already  developed,  will  also  have  application  here,  and  particularly 
in  the  connection  of  the  fundamental  chords  in  minor,  what  was  said 
about  the  progression  of  the  leading  tone  comes  very  distinctly  into  view 
since  the  step  of  an  augmented  second,  occurring  in  the  minor  scale 
between  the  sixth  and  seventh  degrees,  as  well  as  descending,  between  the 
seventh  and  sixth,  is  to  be  avoided  as  unmelodious,  if  both  tones,  which 
contain  the  step  of  an  augmented  second,  belong  to  different  harmonies,  e.  g. 

:=5|:zi=|=f±|:zi:S=FE 


ST. 


1,^1^; 


VI 


VI 


Hence,  in  the  often  recurring  connection  of  the  chords  of  the  fifth  and 
sixth  degrees,  the  progression  of  the  leading  tone  will  be  necessarily  always 
upwards,  whereby,  in  the  triad  of  the  sixth  degree  the  third  appear 
doubled,  e.  g,  \ 


5S. 


Thus,  it  would  not  be  possible  to  exhibit  in  a  correct  form  the  example 
given  under  No.  57  &,  unless  we  make  use  of  a  mediating  tone,  such  as,  for 
example : 


59. 


Remark. — The  practice  deviates,  in  certain  and  especial  cases,  from  this  rule.  It  will 
be  well,  however,  to  accustom  ourselves  to  the  leading  of  the  voices  above  shown,  and 
the  more,  as  we  must  not  overlook  the  fact,  that  every  deviation  from  the  rules  in  the 
practice  is  and  should  be  only  a  well  founded  exception,  whereas  the  observance  of  the 
rule  can  be  instanced  in  numberless  cases. 


<\K 


MANUAL    OF   HARMONY. 


Exercises  in  connecting  the  Triads  of  tlie  Minor  Scale. 


45 


60.  ^ME^~?E^. 


^^ 


l^el 


ef; 


i 


t         5$ 


3     $ 


5.  6. 

^ 5 a      -I _  -^       -  t 


—I Q^ — I ri 


,       Hetnarks  on  these  Exercises, 

A  chromatic  sign  over  a  Bass  note  without  a  figure^  as,  for  example, 
in  the  third  measure  of  the  first  exercise,  refers  always  to  the  third  of  the 
Bass.  This  raising  of  the  third  in  the  dominant  triad,  which  occurs  very 
often  in  minor,  is  the  raising  of  the  leading  tone  spoken  of,  (page  40). 

The  triad  is,  as  a  rule,  not  marked  in  the  thorough-bass  notation,  if  the 
Bass  contains  the  fundamental,  unless  especial  reasons  exist  for  indicating 

K  8 

it  by  3,  5,  8,  or  ^  or  in  full,  by  5 

3 

One  reason  for  indicating  it  by  5,  is  found  in  the  third  and  sixth  exer- 
cises. Here  the  introduction  of  the  triad  of  the  third  degree  in  minor 
has  been  attempted,  whereby  it  was  necessary  to  indicate  that  the  fifth 
is  raised,  since  it  likewise  forms  the  seventh  degree  of  the  minor  scale. 

The  figure  3  or  5  over  the  first  chord  of  some  of  the  examples,  indicates 
its  position.  See,  in  regard  to  this,  the  remarks  to  the  next  exercises, 
(page  50). 

The  working  out  of  an  exercise  will  confirm  the  fundamental  features 
hitherto  developed.     We  select  for  this  purpose  the  first  exercise. 

NB. 


61. 


i^^1ii:^iEL=iJi 


i^^: 


E 


:t 


J- 


i 


The  first  principle  of  the  connection  of  chords  (by  connection  of  tonea 
in  the  same  voice),  is  here  everywhere  observed,  and  for  this  reason  the 


46 


MANUAL    OF   HARMONY. 


Alto,  in  the  third  measure  (at  NB.),  makes  the  faulty  step  of  an  augmented 
second  from  F  to  Gjf. 

In  order  to  avoid  this  fault  (according  to  page  44),  it  will  be  necessary 
to  let  the  Alto  progress  from  F  to  E,  and  to  lead  the  Soprano  from  B  to  G^, 
while  the  Tenor  skips  from  D  to  B,  in  the  following  manner : 


62. 


5gi=EJ=l 


(a  connection  of  chords,  which  has  already  been  explained  in  No.  31, 
where  the  connection  of  tones  does  not  take  place  in  the  same  voice),  or, 
the  Soprano  retains  the  B  and  the  Tenor  goes  from  D  downward  to  the 
GJ(,  the  Alto  from  F  to  E,  whereby  the  close  position  is  forsaken,  and  this, 
and  the  following  harmony  appear  in  open  position  : 


63. 


(I^g^ 


PMm^m 


Farther  remarks,  which  the  difficulties  in  the  leading  of  the  voices  in 
reference  to  the  chords  of  the  fourth,  fifth  and  sixth  degrees  of  the  minor 
scale  render  necessary,  are  in  especial  cases  to  be  left  to  practical  guidance. 

Before  we  proceed  to  the  farther  use  of  the  triads,  we  will  exhibit,  in  the 
following  manner  the  chords  hitherto  discovered  : 


View  of  all  Triads  of  tlie  Major  and  Minor  Scales, 

Major.  ;^f>^yf\'■'^ 

II  III  IV  V  TI  VIlO 

r. 


64. 


I 


Minor, 


-\^-%z^~mi-^%zz=m.- 


I 


nO       IIP       IV         V       VI       viio 
in  Major: 


Major  triads  are  found 


in  Minor: 


—m=.vi 


1 


IV       v 


V        VI 


MANUAL    OF   HARMONY. 

in  Major  : 


Minor  triads 


Diminished  triads 


Augmented  triad 


in  Minor  : 


^=ii^=sEEiri[| 


-^^ 


^ 


II  III  VI 


in  Major  :  in  Minor : 


VIlO 

in  Minor : 


iHIE 


III' 


CHAPTER  III. 

TJie  Inversions  of  tJie  Triads, 

The  Chord  of  the  Sixth,  the  Chord  of  the  Sixth  and  Fourth. 

The  appplication  of  the  triads,  and  indeed  of  all  fundamental  chords,  is 
not  limited  to  that  use  of  them  in  which  the  fundamental  lies  in  the  Bass^ 
as  in  all  previous  examples;  the  Bass  can  also  receive  the  thii'd  ov fifth  of 
the  fundamental  chord.  Hereby  arise  transformations  of  the  fundamental 
chords,  which  are  called 

IN  VERSIOIf  S 
of  the  chord.  ! 

Remark. — It  should  be  well  remarked,  that  only  transpositions  of  the  Bass  to  another 
intervttl  are  here  spoken  of,  and  that  the  before  mentioned  transpositions  of  the  other 
voices  into  close  and  open  position,  and  to  various  intervals,  hy  no  means  essentially  alter 
the  chord.* 

Two  of  the  inversions  are  possible  with  the  triad : 

a.     If  the  Bass  receives  the  third  of  the  triad,  there  arises  the  chorii 

OP  THE  SIXTH. 


Funda'mental  chord.    Chord  of  Vie  sixth. 


65. 


i 


TTiird 
of  the  fundamental  chord. 


The  word  P.  o^.sposki''  n  is  here  used  in  its  general,  not  its  technical  sense.  —Ed, 


48       '  MANUAL    OF   HARMONY, 

ll.     If  the  Bass  receives  the  fifth  of  the  triadj  there  arises  the  chord 

or  THE  SIXTH  AND  FOURTH. 

Fundamental  CJiord 

chord.        of  the  sixth  and  fourth. 

•^  ■*  Fifth  M 

/"■*""""        d 

The  chord  of  the  sixth  is  indicated  by  6  over  the  Bass  note,  that  of  th^^^ 
6 

4' 


sixth  and  fourth,  by . ;  e.  g 


67. 


§i: 


6 
6  4 

:~ gi: 


COG 
C:    I  I  I 


The  letter  shall  in  future  serve  for  indicating  the  fundamental  tone,  and, 
as  before,  the  numeral  to  indicate  the  degree,  whereby,  as  can  be  seen  in 
Example  67,  only  the  situation  of  the  fundamental  tone  can  be  taken 
into  consideration,  not,  however,  the  casual  Bass. 

Remark. — As  the  fundamental  tone  of  the  chords  of  the  sixth  and  of  the  sixth  and 
fourth  in  Example  67,  is  always  C,  and  not  the  Bass  notes  E  and  G,  so  the  chord  itself  will 
not  lie  upon  the  third  or  fifth,  but  upon  the^r*^  degree,  since,  in  fact,  these  are  no  newly 
formed  chords,  but  only  chords  brought  into  another  position  by  the  Bass,  and  therefore 
derived  cliords. 

Every  triad  can  appear  in  such  inversions. 

Application, 

By  the  use  of  the  inversions  of  the  chords,  not  only  does  the  leading  ot 
the  harmony  receive  more  variety,  but  the  movement  of  the  voices,  and 
particularly  of  the  Bass,  becomes  thereby  more  flowing. 

According  to  the  above  noticed  rules  for  the  doubling  of  an  interval  of 
the  triad  (page  25),  it  will  also  be  better  in  the  case  of  the  chord  of  the 
sixth,  in  the  four-voiced  movement,  to  double  the  fundamental  of  the 
original  chords  and  the  doubling  of  the  Bass  tone  in  the  chord  of  the 
sixth  (that  is,  the  original  third),  can  take  place  only  if  the  natural  leading 
of  the  voices  requires  it,  or  if  thereby  certain  faults  can  be  avoided. 
That  the  leading  tone,  even  if  it  lies  in  the  Bass,  is  to  be  excluded  from 
this  doubling,  may  be  yet  remarked  after  what  was  said  on  page  39. 

Just  so,  it  needs  merely  to  be  mentioned,  that  the  position  of  the  upper 
three  voices  is  conditioned  only  by  the  leading  of  the  voices,  and  aside 
from  this,  has  no  essential  influence  upon  the  chord  itself. 


MANUAL    OF    HARMONY.  49 

The  chord  of  the  sixth  can  therefore  occur  in  the  following  forms  : 


6§. 


t-g f — — r-5=rz:^^nrpzz— z= 


-g-F-|— F-§=-F-i— F- 


i; 


i 


&C. 


9iEgEpEgE^E^=^=^Eg^gE^E^ 


The  use  of  the  chord  of  the  sixth  and  fourth  is  more  rare  than  that  of 
the  chord  of  the  sixths  and  requires  certain  conditions  which  shall  be  men- 
tioned later.  "We  meet  it  oftenest  in  the  formations  of  the  close.  The 
Bass  tone,  the  fifth  of  the  original  chord,  is  best  adapted  for  doubling,  and 
tlie  chord  will  appear  in  the  following  and  similar  forms  : 


69. 


mi=m^ 


lE^^m^^m 


In  the  connection  of  these  chords  with  others,  no  farther  mechanical 
rules  are  necessary  beyond  those  already  given ;  we  likewise  omit  the  mere 
mechanical  combination  of  two  or  three  chords,  and  show  the  application 
of  these  derived  chords  in  small  pieces  of  music,  which,  however  insignifi- 
cant, still  contain  the  image  of  a  whole,  whereby  individual  cases  can  be 
better  judged  of  in  relation  to  the  whole. 

Exercises. 


70. 


^JE^: 


la: 


ee; 


m 


mi 


i^?=?ii=E=!^ 


^B=3i 


llalliP^J 


-si — s 


6        6 


cv=^_z=!==,2:zp:3ii:©-I=:^==^^==^=:s 


— ^ 


EtEEi 


i 


9i^ 


ns: 


6       6 
-5, G- 


R  6 

4—^ 


6       6 


3$; 


i^E^ 


^ 


50 


MANUAL    OF    HARMONY. 


6       6 


n.     3 


eS^ 


:e 


G 


6 
4  3 


igEt 


1 


l^jEa= 


:^=± 


»•        6      6         t       6 

4 


3      6         6 


^eI^^Hf^^ 


c^ 


^E^EE^z-P-EZgE 


JSr      6     ^      « 

tit 


10. 


1-^- 


6     jsr 


6 

4$ 


s.^l^l=i-^li^l^l-sl=S 


11. 


9iiE$^:E?=^=E 


1^-^- 


=1=^^ 


Ie 


\ 


Memarks  on  these  Exercises, 


The  indication  of  the  fifth  in  the  first  measure  of  the  second  Example, 
as  also  all  similar  indications  in  the  future,  denote  the  situation  of  the 
Soprano,  and  therewith  the  position  of  the  first  chord.  If  no  figure  stands 
over  the  first  Bass  note,  it  is  to  be  assumed,  that  the  Soprano  can  best 
receive  the  octave  of  the  Bass. 

The  diminished  triad  appears  in  the  second  exercise  as  chord  of  the 
sixth.  It  occurs  oftenest  in  this  situation.  It  may  here  be  called  to  mind 
that  its  fundamental  tone  is  not  doubled,  because  of  its  being  the  leading 
toncy  whereas,  in  most  cases,  the  third  (in  the  chord  of  the  sixth  the  Bass 
tone)  is  doubled.  The  leading  of  the  voices  occasions,  sometimes,  also  a 
doubling  of  the  fifth. 

The  progression  of  the  diminished  triad  is  always  conditioned  by  the 
leading  of  the  Bass.  The  natural  direction  of  the  diminished  triad  in  its 
fundamental  position  is  already  given,  page  38. 

In  the  most  usual  cases  the  progression  of  the  Bass  is  as  follows  * 


Tl 


^^^^^ 


and  the  progression  of  the  remaining  voices  thus : 


72, 


Sr|r::g^:^=:ga:e=rgit:g=:giE:B:z::gJ:g-^-3-tf— «-EE 


gg^^JEgfJE^^g 


:=P=:4 


:t:=t:: 


i^llE 


MANUAL    OF    HARMONY. 


51 


It  is  evident  from  the  above  Examples,  that  the  inversion  of  the  dimin- 
ished fifth,  viz.,  the  augmented  fourth,  will  not  necessarily,  in  four -voiced 
movement^  have  the  same  progression  as  was  given  above,  two-voiced,  page 
08.     We  see,  in  the  first  example  and  others,  B  and  F  of  the  Soprano  an 
Alto  progress  to  C  and  G. 


73. 


^ 


The  similarity  of  this  chord,  in  sound,  to  the  dominant  chord  of  the 
seventh  to  be  shown  later,  often  induces  beginners  to  lead  the  diminished 
fifth  downwards^  even  if  it  has  converted  itself  by  inversion  into  the  aug- 
mented fourth ;  this,  as  the  above  examples  show,  is  necessary  only  in  caoe 
it  really  lies  above  the  fundamental  as  diminished  fifth,  and  a  progression 
of  the  following  sort : 


T4. 


flSMB 


S; 


HI 


is  faulty  on  account  of  the  parallel  fifths. 

Remark. — It  may  yet  be  remarked  here,  that  parallel  fifths,  of  whidh  the  one  fifth  is 
diminished  and  the  other  perfect,  are  to  be  allowed  if  the  diminished  follows  the  per- 
fect ffth,  but  not  vice  versa,  e.  g. 


good. 


good. 


not  good. 


T5, 


9t 


6  6  6  3 


i; 


I 


Compare  also  the  Remark,  page  28. 

The  progression  of  the  voices  takes  another  form  in  the  diminished 
triad,  if  the  Bass  goes  over  to  a  chord,  other  than  the  tonic  triad.  A  few 
chord-connections  may  follow  here  : 


70. 


not  pure. 
-Gh Q- 


fr^l 


|^^^E|^|EfE|^|E^ 


P 


VIlO 


TIl«        IV 


M 


— G- 


vuo 


p 


52 


MANUAL    OF   HARMONY. 


H 


letter . 


not. 


«9- 


6 


m^pi^^ 


m 


^^^-^ 


m 


^mm 


-I o ^ — r — 


'i^ 


ii 


i 


VIlO        II 


and  others. 


The  diminished  triad  of  the  second  degree  in  Minor  allows  another 
treatment,  since  its  fundamental  can  be  doubled. 

The  succession  of  two  or  more  chords  of  the  sixth,  with  a  progression  of 
the  Bass  by  degrees,  as  in  Exercise  70,  No.  3,  and  others,  will  render 
necessary  one  or  more  voices  mV)ving  in  contrary  motion  to  the  Bass,  e.  g. 


f 


s=feisa=^^^'3=y 


The  series  of  chords  of  the  sixth  of  the  5th  and  6th  Exercises  in  No.  70 
can,  to  be  sure,  be"  carried  out  in  various  ways ;  best,  however,  if  the  con- 
sequent succession  of  the  Bass  is  retained  also  in  the  remaining  voices,  e.  g 


7§. 


m^m 


:i 


i=t:g 


s_^=:=:|; 


^^=EE|Ep 


-O (J»- 


1 


6        6 


:E=t: 


&C. 


i 


Covered  octaTes,  as  in  the  2d  and  3d  measures  between  Tenor  and  Bass, 
are  not  to  be  avoided  in  such  cases.  It  can  be  deduced  from  this,  that  to 
SINGLE  progressions  of  the  voices  which  are  contrary  to  rule,  that  especial 
importance  is  not  to  hd  attached,  in  opposmoN  to  the  consequence  of 
THE  WHOLE,  which  otherwisB  belongs  to  them^  since  the  construction  of  the 


MANUAL    OF   HARMONY. 


53 


details,  although  it  must  be  as  perfect  as  possible,  will  always  be  subordi- 
nate to  that  of  the  whole. 

Remark. — It  is  not  to  be  ignored,  that  the  principle  laid  down  above  can  easily  be 
misunderstood  by  the  beginner ;  however,  the  laying  down  of  the  principle  was  not  to 
be  evaded,  and  it  may  be  added  here,  in  order  to  avoid  possible  error,  that  a  decision  in 
these  things,  in  the  last  instance,  belongs  only  to  a  judgment  fully  matured  by  expe- 
rience and  practice. 

Concerning  the  Signs  of  the  Thorough-Mass  Notation, 

The  numbers  and  signs  of  the  Thorough-Bass  are  called  in  general  sig- 
natures^  [in  German  works  Signaturen. — Ed.]  Some  of  them  have 
already  been  explained,  as  the  chromatic  sign  occurring  very  often  in  minor. 
The  notation  of  the  chords  of  the  sixth  and  of  the  sixth  and  fourth  was 
given,  page  48.  A  stroke  through  the  figure  is  used,  (for  example,  in  the 
Exercises  8,  9,  10,  of  No.  70,  a  stroke  through  the  6  :  0),  if  a  chromatic 
elevation  of  the  interval  a  half-step  becomes  necessary ;  instead  of  which, 
however,  a  }f  or  t]  is  often  set  after  the  figure  [e.  g.^  6:j$  or  6t),  5t].)  Other 
figures  will  find  their  explanation  later  in  connection  with  the  chords 
which  they  concern. 

Formation  of  the  Close  through  tJ^  Chord  of  the  Sixth  and 

Fourth, 

In  the  Exercises  of  No.  70  we  see,  through  the  inversion  of  the  triad, 
the  formation  of  the  close  previously  mentioned,  extended  and  put  into  a 
much  more  definite  shape.  We  discover,  namely,  that  the  chord  of  the 
sixth  and  fourth  of  the  tonic  triad,  coming  before  the  dominant  triad,  indi- 
cates decidedly  the  close. 


79. 


The  chord  of  the  sixth  and  fourth  is  frequently  preceded  by  the  triad 
of  the  fourth  or  second  degree. 


80. 


54  MANUAL    OF   HARMONY. 

As  decidedly  now  as  the  chord  of  the  sixth  and  fourth  indicates  the 
close,  having  also  a  decided  influence  in  the  modulation  into  foreign  keys, 
just  so  weak  is  the  effect  of  its  entrance  under  other  relations,  so  that  its 
proper  use  is  subject  to  certain  conditions,  which  will  be  treated  of  later. 


CHAPTER    ly. 

Harmonies  of  the  Seventh  ( Vierkldnge), 

The  harmonies  of  the  seventh  are  founded  upon  the  triads.  They  result 
from  the  addition  of  a  third  to  the  fifth  of  the  triad,  which  [third]  forms  a 
seventh  from  the  fundamental. 


81. 


Not  only  the  various  kinds  of  triads,  but  also  the  various  kinds  of 
sevenths  will  afford  manifold  harmonies  of  the  seventh. 

The  General  Properties  of  the  Chords  of  the  Seventh, 

The  chords  of  the  seventh  arfr  not  so  independent  as  the  most  of  the 
triads,  but  indicate  definitely  a  progression,  so  that  they  never  alone,  but 
only  in  connection  with  triads,  afford  anything  complete  or  finished.  On 
the  other  hand,  they  will  render  the  relations  of  the  chords  to  each  other 
closer  and  more  intimate,  and  by  means  of  this  quality  furnish  in  particular 
excellent  means  for  the  connection  of  chords  and  for  the  leading  of  the 
voices. 

The  Dominant  Chord  of  the  Seventh  in  Major  and  Minor. 

The  chord  of  the  seventh  which  is  most  important,  and  occurs  oftenest 
is  the 

DOMINANT  CHORD  OF  THE  SEVENTH, 

also  called  primary  chord  of  the  seventh. 

It  rests,  like  the  dominant  triad,  upon  the  fifth  degree,  and  is  formed 
xactly  alike  in  major  and  minor,  that  is,  /row  the  major  triad  and  minor 
Seventh. 


•^ C:    V        V  c:    V        V^ 


I 


MANUAL    OF    HARMONY. 


55 


In  the  fundamental  position  it  is  marked  by  a  7  over  the  Basu  note,  and 
in  our  method  of  notation,  indicated  by  V7 


83. 


n 


C:    V 


G:    V. 


The  relation  in  which  the  triad  of  the  dominant  stands  to  the  tonio 
triad,  has  become  clear  principally  through  the  formation  of  the  close 
shown  before,  (see  page  33).  The  close  will  come  out  still  more  clearly 
through  the  use  of  the  dominant  chord  of  the  seventh. 

The  following  combination  of  chords  will  show  the  formation  of  the 
elose : 


84. 


Remark. — It  is  to  be  remarked  here,  that  the  triad  following  the  chord  of  the  seyentb 
is  ineomplete  ;  in  both  eases  the  fifth  of  the  triad  is  wantiug.  The  reason  of  this  will 
appear  from  what  follows. 

The  striving  after  a  point  of  rest,  inherent  in  these  chords,  and  the 
resulting  union  with  a  triad,  is  called 

RESOLUTION  OF  THE  CHORD  OF  THE  SEVENTH,  {Cadence). 

If  the  union  of  the  dominant  chord  of  the  seventh  with  the  tonic  triad, 
follows  in  the  manner  exhibited  in  No.  84,  or  in  a  similar  way,  it  is  called 
CLOSING    CADENCE. 
For  the  leading  of  the  voices,  the  progression  of  the  intervals  of  the 
chord  of  the  seventh  will  furnish  important  observations. 

We  observe  first  the  closing  cadence  as  the  regular  resolution  of  the 
dominant  chord  of  the  seventh  especially. 

The  seventh,  as  the  essential  interval  of  the  chord,  is,  by  its  relation  to 
the  fundamental,  confined  to  a  definite  progression.     If  the  progression  of 
'tiie  Bass,  which  contains  the  fundamental,  is  regarded  as  given,  an  upward 
jjrogression  of  the  seventh  will  appear  impossible : 


§5. 


^ 


MANUAL    OF   HARMONY, 


«veii  if,  as  at  h^  a  third  voice  is  added  ;  whereas  its  downward  progression 
<iffords  full  satisfaction : 


1 


§6. 


I 


-o-^-^ 


*^ 


1 


Since  the  progression  of  i\iQ  fundamental  by  an  upward  step  of  a  fourth 
or  downward  step  of  a  fifth  is  already  determined,  the  progression  of  the 
third  and  fifth  of  the  chord  of  the  seventh  remains  to  be  considered. 

j?%e  third  of  the  dominant  chord  of  the  seventh  is  always  the  leading 
tone  of  the  , scale  ;  its  natural  direction  is  therefore  determined  by  what 
has  been  said  before  concerning  the  leading  tone,  (page  39) ;  its  progression 
will  follow  a  half-step  upwards,  and  h  will,  therefore,  not  appear  so  nat- 
ural as  a : 


»T. 


-JSIZ 


mm 


iiiilliii^IE 


In  the  Example  87,  &,  the  third,  is  given  to  the  upper  voice,  which  ren- 
der the  unpleasantness  of  its  progression  quite  perceptible.  This  leading 
becomes  tolerable  if  the  third  is  found  in  a  middle  voice,  6.  g. 


I 


6. 


1^111=^18 


8S. 


lilliE^iill 


,  This  downward  leading  of  the  third  (leading  tone)  is  therefore  to  be 
applied  under  the  following  conditions  : 

a*     If  it  does  not  lie  in  the  upper ^  hut  in  a  middle  voice,  e.  g, 

seldom  practicable. 


89. 


9! 


I 


MANUAL    OF    HARMONY.  67 

\ 

ll»     If  the  Bass  progresses  in  contrary  motion^  e.  g, 

b.       not : 


90. 


The  reason  of  the  second  rule  becomes  evident,  if  we  observe  the  cov- 
ered fifths  in  the  last  Example  b^  between  Alto  and  Bass. 

The  leading  of  the  Jifth  of  the  chord  of  the  seventh  is  free.  "VVhile^ 
for  the  most  part,  it  is  crowded  a  degree  downwards  by  the  seventh,  reasons 
may  exist  connected  with  the  leading  of  the  voices,  for  allowing  it  to  pro- 
gress a  degree  upwards,  as  Example  88  b  shows,  where  the  D  of  the  So- 
prano is  lead  to  the  E. 

If  we  condense  these  remarks,  we  find  the  following  rules  for  the  regu- 
lar resolution  of  the  chord  of  the  seventh,  and  for  the  closing  cadence  in 
particular : 

The  seventh  progresses  a  diatonic  degree  downwards,  while 
The  fundamental  makes  a  ship  of  a  fourth  upwards  or  a  fifth  down 
wards ;  ' 

Just  so  the  third  is  led  a  degree  upwards  toicard  the  seventh^  while 
The  fifth  can  he  led  hy  degrees^  upward  or  downward. 

Remark. — By  the  progression  of  the  third  towards  the  seventh,  we  are  reminded  of 
what  was  said  of  the  fundamental  and  the  diminished  fifth  in  the  dimmished  triad,  (page 
S8).    Both  intervals  are  found  again  in  the  dominant  chord  of  the  seventh. 

Application. 

Except  in  the  formation  of  the  closes,  the  dominant  chord  of  the  seventh 
is,  in  the  middle  of  a  piece,  seldom  employed  in  the  usage  thus  far  known 
to  uSy  and,  if  it  does  take  place,  only  in  a  position  whereby  the  feeling  of 
the  complete  dose  is  not  produced. 

This  takes  place  particularly  in  cases  where  the  seventh  of  the  chord 
lies  -in  the  upper  voice,  whereby  the  close  becomes  incomplete,  or,  if  the 
dominant  chord  of  the  seventh  falls  upon  the  accented  part  of  the  measure 
(thesis),  since  in  the  complete  close  (cadence)  the  tonic  triad  must  fall 
there.     (See  page  33). 

Besides  this,  the  chord  often  appears  incomplete  through  the  omis&ion 
of  an  interval.  This  interval,  however,  can  only  be  the  Jifth,  seldom  the 
third,  while  the  omission  of  the  fundamental  or  the  seventh,  would  entirely 
alter  the  chord,  and  render  it  incapable  of  recognition.  ^^ 


58 


91. 


MANUAL    OF   HAltMONY. 
b.  c,  rarely:  d. 


In  a^  bf  df  the  fifth  is  omitted,  in  c^  the  third,  and  in  each  case 
the  fundamental  doubled  instead,  which  doubling  affords,  by  means  of  the 
tone  which  is  allowed  to  remain  stationary,  the  closest  connection  with  the 
following  chord,  and  allows  the  tonic  triad  to  appear  again  complete, 
which  was  not  the  case  in  the  previous  resolution.     (See  No.  84). 

We  add  the  following  remark  upon  the  omission  of  an  interval  in  the 
chord  : 

Through  the  leading  of  the  voices  a  chord  can  appear  incomplete  ;  the 
omitted  interval  will,  in  most  cases,  he  the  fifth  of  the  fundamental  chord. 


Exercises, 


92. 


&^i^|3 


7 


G       6 


6 

4      7 


I^CIZ^ 


ir=g 


^1^ 


6        6 


ilEg: 


— I &- 


EE 


li^ip^l^^Jlil 


3.      ^  6       6 


gl^=^j=EE|: 


6 
43 


6 
47 


giiE^=gEEgE|i^-3E 


.p^:Jir 


Pi 


5.       3      6 

-j:L 


7  6 

t  6       4 

-49—1 


6      7 
4       % 


gg$;^^E|EgEEg|E^5|gEJ; 


:qz=:1=::=5 


-¥- 


^^1=1 


EE5 


J8'      6 


67 

4« 


^^^feziiE^=!E|^El^E^E|^^iE^| 


These  exercises  require  no  farther  explanation.      It  has  been  already 
mentioned,  that  the  chord  of  the  seventh,  in  the  position  known  to  us  now. 


MANUAL    OF    HARMONY. 


59 


is  indicated  by  7,  also  that  the  sharp  found  under  it,  or  in  general,  all 
chromatic  signs  which  occur  without  figures  opposite  to  them,  have  refer 
ence  to  the  third  from  the  Bass  tone.     (See  page  55.) 


CHAPTER    V. 

The  Inversions  of  the  Chord  of  the  Seventh, 

Like  the  triad,  the  chord  of  the  seventh  can  be  altered  in  such  a  man. 
ner,  that  the  Bass  receives  an  interval  other  than  the  fundamental. 

The  first  inversion  arises,  if  the  Bass  receives  the  third  of  the  funda- 
mental ; 

The  second,  if  the  fifth  of  the  fundamental  chord  lies  in  the  Bass,  and 

The  third,  if  the  original  seventh  is.given  to  the  lower  voice. 

In  close  position  the  inversions  present  themselves  thus  : 


93. 


^ 


-&fi — -«^- 


I 


A  comparison  (Jf  these  inversions  of  the  chord  of  the  seventh,  with 
those  of  the  triad,  shows  plainly  their  analogous  position  : 


94, 


i^^: 


\^ 


These  derived  chords  receive  their  designation  from  the  position  of 
their  intervals : 

ThQ  first  inversion  is  called  the  chord  of  the  sixth  and  fifth. 

The  second  :  the  chord  of  the  sixth,  fourth,  and  third,  or  briefly,  chord 
of  the  fourth  and  third. 

The  third  :  the  chord  of  the  sixth,  fourth, and  second,  or  briefly,  chord 
of  tJie  second. 

Their  designation  in  the  Thorough-Bass  notation  is  to  be  seen  above,  in 
Exampp  94. 


60 


MANUAL    OF   HARMONY, 


It  needs  only  to  be  remembered  here,  that  in  these  inversions,  just  as 
before  in  the  inversions  of  the  triad,  only  the  position  of  the  Bass  or  of 
the  lowest  voice  is  essential,  and  that  the  remaining  intervals  can  be  vari- 
ously distributed  among  the  upper  voices,  e.  g. 


95. 


I 


:^: 


12?=! 


:i:= 


m 


— 6»— 


mm^m 


p 


le: 


■.T=.=r—?s=:-i 


^m^^^, 


G— 
-G— 


i 


77 


&c. 


^fe^l=l=l=l=[^^ 


2  2  -  -  - 

Application, 

The  regular  progression  (resolution)  of  these  derived  chords  is  founded 
upon  that  of  the  fundamental  chord. 

If,  in  its  case,  the  dissonance,  the  seventh,  conditioned  the  progression 
in  one  direction,  the  tendency  to  the  same  progression  (resolution),  will 
also  exist  in  the  case  of  the  derived  chords,  in  which  the  two  tones,,  the 
fundamental  and  the  seventh,  either  appear  again,  or  become  seconds  by 
inversion. 


96.    p 


:s?: 


i^i 


:b?j 


i 


Progression  of  the  Chord  of  the  Sixth  and  Fifth, 

Since  the  original  seventh  shows  itself  likewise,  over  against  the  Bass 
tone  in  the  chord  of  the  sixth  and  fifth,  as  dissonance,  as  diminished  fifth, 
the  progression  of  which  was  discussed  above,  (page  38), 


97. 


g2=g^=fl 


the  resolution  of  the  chord  of  the  sixth  and  fifth  will  naturally   take 
place  thus  : 


9§. 


MANUAL    OF    HARMONY.  6J 

% 

The  progression  of  the  fundamental,  as  before  given,  does  not  appeal 

here,  since  the  Gr  of  the  upper  voice  is  sustained  and  transforms  itself  into 
the  fifth.  This  is,  however,  only  apparent,  for  that  it  forms  the  foundation 
of  this  connection  of  harmony,  the  marking  below  G7  C,  of  Example  98 
proves. 

That  however,  the  Soprano,  or  a  middle  voice,  cannot  in  notes  carry 
out  the  progression  of  the  fundamental  in  such  cases,  lies,  beside  other 
reasons,  immediately  in  the  character  of  these  voices,  which  is  to  be  found 
more  in  mediation  and  connection  of  the  harmonies,  than  in  laying  their 
foundation,  which  belongs  to  the  Bass. 

Remark. — Deviating  progressions  of  the  fundamental  in  these  cases,  such  as  a  freer 
leading  of  the  voices  in  certain  relations  -would  give,  are  not  hereby  excluded,  only  there 
must  be  an  inner  connection  of  the  chords. 

Progression  of  the  Chord  of  the  Sixth,  Fourth,  and  Third* 

We  find  again  here,  beside  the  seventh  and  its  inversion,  the  diminished 
fifth  or  its  inversion,  the  augmented  fourth  : 


►.9 


99.   z^^znz^ 


The  resolution  of  this  chord  follows  thus  : 

a.  6. 


100. 


^^Szl^l^^^^ 


The  Bass,  the  original  fif^h,  can  progress  in  both  of  the  given  ways. 
Progression  of  the  Chord  of  the  Second, 

This  chord  has  the  peculiarity,  that  the  original  dissonant  intervals,  the 
seventh  and  the  diminished  fifths  can  only  occur  in  their  inversions,  as 
second  heloiv,  and  augmented  fourth  helow. 

The  progression  of  this  chord  is  as  follows : 


101. 


2  6  2  6 


7  7 


Thus  the  resolution  of  the  chord  of  the  second  is  eflfected  here  through 
the  chord  of  the  sixth. 

We  can  perceive  in  these  resolutions,  that  they  are  all  based  upon  the 
natural  progression  of  the  dominant  chord  of  the  seventh,  which  before 


0-2 


MANUAL    OF   HARMONY. 


was  called  cadence^  for  we  find  everywhere  the  same  marking  of  the  funda- 
mental G7  C  or  V7  I. 
/       These  resolutions  will,  therefore,  themselves  form  cadences^  only  not  of 
j  ro  complete  a  sort  as  those  mentioned  above,  and  as  those  are  C2X\qA  perfect 

View  of  the  Natural  Progression  of  all  Inversions  of  the  JDoni' 
inant  Chord  of  the  Seventh  in  various  positions. 


a. 


The  Chord  of  the  Sixth  and  Fifth. 


102. 


=E=i^S3EEE=^E_^i^: 


P= 


©- 


lez: 


6 
5 

£2. 


I 


fo.     The  Chord  of  the  Sixth,  Fourth,  and  Third. 
or: 


I^^^eM^^^M^^ 


JB 


©- 


"'z-s: 


3. 


^^ 


4 
4  3 


MANUAL    OF    HARMONY. 


63 


C.     The  Chord  of  the  Second. 


i] 


9i 


^E;E!|5^FEe|i^p^S:gEEggfi^FE^!E^E:] 


Exercises  in  the  Use  of  these  Chords, 

6 

5  6       6  3  2  6 


6 

4  7 


103 


► 


4                        '6 
_    2.         3  a       C  6      5  6       87 

4  6  6 

3.  5  3263  5  47 

6  6       87 


-\ 


§LiEg; 


4  6 

2       6  3      6  4  3  6 


-.tzzi^zz 


'i^ll^ilif^lii 


87 
6       t 


-©-—(2 


^z:±zzf:z=:t=J:iza: 


2        6  F 


67 

4J 


iniii^^pi 


J=:3^^: 


:t=:i 


11151=1 


4 

3       6 


WI^^e:^: 


!^ 


67 

6  41 


|g^gE|E^E|E|E|Ei=p-:^j 


9iP=^: 


'=EE: 


#        -,  32         6       3 


67 

4« 


EE=^ 


^^^^^^^i^^ 


Observation. — The  marking  8  7  in  the  next  to  the  last  measure  of  the 
second,  fourth,  and  fifth  Examples,  denotes  that  the  seventh  should  not 
appear  with  the  chord  itself,  but  follow  after  the  octave. 


- ,  U  r-Z^f^"^. 


64  MANITAZ    OF    HARMOITT. 


CHAPTER    VI. 

Secondary  Harmonies  of  the  SeventJi, 

"While  in  the  case  of  the  triads,  three  primary  chords  are  requisite  to 
establish  the  key,  (the  relation  to  the  tonic  triad  as  central  point),  there  is 
needed  in  the  case  of  the  chords  of  the  seventh,  only  one  primary  chords 
the  dominant  chord  of  the  seventh,  the  content  of  which  alone  already 
renders  the  key  certain,  and  the  natural  progression  of  which  to  the  tonic 
triad  represents  the  key. 

Remark. — The  manifest  fact,  that  the  seventh  of  the  dominant  chord  of  the  seventh 
is  at  the  same  time  fundamental  of  the  subdominant  triad,  renders  the  relation  of  the 
two  tones  G  and  F,  (as  fundamentals  of  the  dominant  triads),  to  their  common  centre, 
C,  (as  tonic  triad),  already  entirely  clear.    (See  above,  page  22,  3). 

Beside  this  dominant  chord  of  the  seventh,  also  called  primary  or 
essential  chord  of  the  seventh,  harmonies  of  the  seventh  can  be  formed 
from  the  remaining  triads  in  major  and  minor,  the  relation  of  which  to  a 
definite  key  is  indeed  undeniable,  but  by  no  means  so  decided  as  in  the 
case  of  the  primary  chord.     They  are  called 

SECONDARY  CHORDS  OF  THE  SEVENTH. 

They  are  to  be  formed,  simply  by  the  addition  of  a  seventh  of  the  fun- 
damental to  the  triads : 


a.    In  Major: 


104. 


:i=r 


II -r        iiw        IV /r  VI  ly        VII*' 


b.    In  Minor: 
NB.  NB. 


We  come  here  to  chord  formations,  which,  in  part,  without  connection 
with  other  chords,  sound  very  harsh,  and,  for  this  reason,  foreign,  because, 
as  was  already  remarked  above,  their  relation  to  a  fundamental  key  is  not 
so  decided  and  clear  as  that  of  the  dominant  chord  of  the  seventh.  Their 
use  will,  therefore,  be  in  part  more  rare,  but  not  the  less  adapted  for  im- 
parting variety  and  especial  coloring  to  the  harmonic  succession. 

Among  these  secondary  chords  of  the  seventh,  the  following  kinds  may 
be  distinguished : 


MANUAL    OF   HARMONY.  65 

in  Major:  in  Minor'. 

H.     Major  triads  ivith  major     -^«    IjE' g       ~^ F ^ 1 F 

seventh.  '  ^=:|:=^:=:tz=zg:iziiLt 

C:    l;j.        IV^         a:    YI;7< 

NB.     Major  triads  ivitJi  minor  seventh  always  form  dominant  chords 
of  the  seventh. 

■  -m.         TUT'  J    •     7        -,7        n  i^^inor; 

D,     Minor  triad  with    ^j 


major  seventh.        Jsv      Sg  not  used  as  fundamental  harmony. 

in  Major :  in  3  fin  or 

C,     Minor  triads  with  minor 


seventh. 


m^Mimmii 


C:    iiiy        iii-j-       VI ly  a:    ivy 

in  Major  :  in  Minor  . 

cl.     Diminished  triads   with  minor 
seventh. 


•^    C:    viiOiy         a:    iiO^ 


Diminished  triad  with   diminished  seventh. 


!"•     The   augmented   triad  with   major   seventh^ 


in  Minor: 


a:    viiO-' 


a:   my 


as  it  is  found  upon  the  third  degree  in  minor,  is,  to  be  sure,  not  useless, 
but  from  reasons  before  developed  in  the  case  of  the  augmented  triad,  is 
very  seldom  used,  and  ambiguous. 
Remark. — We  find  this  chord  again,  with  another  foundation,  in  Chapter  X. 

Application  of  the  Secondary  Chords  of  the  Seventh  in  3Iajor, 

The  seventh  or  its  inversion,  the  second^  may  be  major,  minor,  dimin- 
ished, or  (which  concerns  the  second  only)  augmented  ;  it  will  always  in  its 
relation  to  the  fundamental  press  as  dissonance  to  a  progression. 

This  natural  progression  is,  with  the  secondary  chords  of  the  seventh, 
no  other  than  that  already  found  in  case  of  the  dominant  chord  of  the 
seventh^  viz.,  one  degree  downwards  toward  the  fundamental,  if  the  latter 
moves  by  fifths  or  fourths,  downward  or  upward. 

If  accordingly  the  progression  of  the  principal  intervals  of  the  chord  is 
found, 


106. 


f=PEt=p*i^^lE^ 


66 


MANUAL    OF   HARMONY. 


I 


for  the  remaining  intervals,  no  new  rule  is  necessary ;  tlie  third  will  bo 
led  one  degree  upward,  while  the  progression  of  the  fifth  can  be  in  either 
direction. 

a,  h.  c. 


107. 


i^^iiaiiiiilPJ^l^ 


^^mmm^^mi^^^ 


C:    I- 


IV 


Vfv  XV  _ ^—  II  ,y  V  

Remark. — ^The  deviation  from  this  rule  in  the  progression  of  the  third  in  Example 
107  hf  is  occasioned  by  the  circumstance,  that  the  covered  octave,  which  would  appear 
in  the  regular  ascension  of  the  third  a  whole  step,  e.  g., 


10§. 


^ 


I 


l\ 


m 


mmmw 


was  avoided  thereby.     See  page  35,  Example  32. 

Whether,  however,  as  in  Example   107  c,  the  leading  tone  should  be  doubled  in  the 
succeeding  chord,  or  the  following  covered  fifths  be  preferred, 


109. 


H 


=ii= 


-0-=^^e- 


l\ 


S,—i 


■will  depend  upon  circumstances  which  can  only  be  judged  of  in  the  application  to  par 
ticular  cases. 


Natural  (Cadencing)  Progression  of  the  Secondary  Chords  of  the 
Seventh  in  3Iajor, 

a.   of  the  first  degree. 


not: 


110. 


2:^^=z=r 


C:    I. 


good: 


IV 


not: 


-.zzoss:- 


i^i^i 


^ 


or:  not: 


MANUAL    OF   HARMONY. 

tcith  omission  of  the  fifth : 


67 


E¥i^^^i^^^^^E^= 


s 


Si^t 


^^^^^m 


b.   of  the  second  degree. 


mm 


-G T 


g—  i:^ — — r-. 


-•g^ 


2:z=:zzi: 


g— 

C:    II Y 


g. 


w^m. 


not. 


not : 


without  fi^fth 


m^^=m^ 


§r 


not: 


9^ — g  t r —  ^~ 

1 — o L 


c.    q/"  <^  third  degree. 


xcithout  fifth : 


wm^mmm^^^^ 


^-T-« 


m^m^^mmm^^ 


not : 
C:    iii-y       VI 


not. 


not: 


of  the  fourth  degree  {seldom  icith  Vus  resolution). 


MaHil^li 


not  good. 

-a. 


^:^iei^i 


s. 


not : 
C:    lY;^. 


VIlO 


not: 


='^^-- 


wiffiout  fifth  : 


^^^^^ 


---^:§_, 


^=^i^PgPi^^ 


^10^  , 


68 


MANUAL     OF   HARMONY, 


e,    of  the  sixth  degree. 


icithoui  fi/lh: 


1^^; 


0-1 


A  HI     A^ 


IHi^^l^iil^ii 


C:    Yiir      n 


not. 


not: 


not. 


f.    of  the  seventh  degree. 


not  good: 


;i^ 


C;    vii°>r      III 


tcithout  ffth : 


^^^ 


^^m. 


not: 


Eemark. — The  above  found  progressions  of  all  chords  of  the  seventh  are  neither  in 
their  positions  exhaustive,  nor  have  they  been  exhibited  as  the  only  possible  ones. 

The  difficulty  of  forming  such  progressions  lies  only  in  the  frequently  occurring 
covered  fifths  and  octaves.  All  the  remarks  also,  which  are  added  above,  such  as  "  not," 
" not  good"  which,  for  the  most  part,  refer  to  the  leading  of  the  Bass,  (inasmuch  as  this, 
with  other  necessary  voice-progressions,  produces  these  faults,)  are,  in  many  cases,  only 
to  be  understood  from  a  theoretical  stand  point,  while  such  cases  and  similar  ones  in  the 
practice,  even  in  the  so-called  pure  harmonic  structure,  must  often  be  judged  according 
to  the  principle  before  expressed,  (pages  52  and  53). 

Since  the  theory  has  not  yet  succeeded  in  furnishing  positive  rules  for  all  cases  of  the 
kind,  the  true  and  false,  the  admissible  and  inadmissible  in  this  respect,  can  only  be  dis- 
tinguished by  means  of  complete  harmonic  education  and  a  really  musically  educated  ear. 
More  about  this  follows  later. 


Concerning  the  especial  Progression  of  the  Chord  of  the  Seventh 
of  the  seventh  Degree, 

In  the  above  found  collection  of  the  progressions  of  all  chords  of  the 
seventh  in  major,  under  No.  110,  that  of  the  seventh  degree^  analogous  with 
the  others,  has  been  led  to  the  third  degree^  that  is,  the  progression  of  the 
fundamental  takes  place,  as  with  the  other  chords  of  the  seventh,  through 
a  step  of  a  fourth  upward  or  a  fifth  downward.     This  progression  is  the 


MANUAL    OF   HARMONY 


09 


more  unusual  one,  and  is,  for  the  most  part,  only  used  in  a  leading  of  the 
harmony  according  to  a  certain  formula  (sequence).  That  progression 
occurs  oftener,  upon  which  the  diminished  triads  to  which  here  the  seventh 
is  added,  is  based,  (see  page  38  and  50),  viz.,  that  to  the  tonic  triad. 


li 


^i 


C:  viio 


VI 1° 


■SE: 


va*f 


m 


m\ 


The  above  Example  shows  plainly,  that  the  relation  of  the  diminished 
triad  to  the  tonic  triad  is  not  altered  by  the  addition  of  the  seventh,  but 
on  the  contrary,  becomes  more  decided. 

It  is  likewise  to  be  remarked,  that,  if  the  chord  appears  in  the  above 
position,  the  third  oi  the  following  triad  must  be  doubled,  (see  No.  Ill  &), 
because  otherwise,  perfect  fifths  would  arise  ;  (See  No.  112  ct), 


I 


112. 


or  a  skip  must  be  used,  as  at  h^  a  leading  of  the  Tenor  which  is  often 
found,  and  which,  in  spite  of  the  covered  octave,  is  very  effective. 

It  is  peculiar  to  this  chord,  that  only  that  position  of  it  in  which  the 
seventh  lies  in  the  upper  voice  produces  a  satisfactory  effect,  while  the 
other  positions,  if  not  impracticable,  still  appear  less  clear. 


113. 


P 


H 


1 


Remark. — Whether  the  reason  of  this  is,  that  in  the  seventh  with  its  above  used 
progression,  the  character  of  the  ninth  lies,  (as  some  theorists  assert,  that  the  dominant 
chord  of  the  seventh,  Avith  added  ninth,  is  the  basis  of  this  chord  with  its  resolution), 
which,  though  similar  to  that  of  the  seventh,  is  still  much  more  comprehensive,  and 
does  not  bear  the  situation  in  the  middle,  cannot  here  be  furtlier  investigated. 


70  MANUAL    OF   HARMONY. 

The  Freer   Treatment  of  the  TJiird  and  Fifth  in  the  Chord  of 

the  Seventh, 

Various  progressions  of  these  intervals  have  already  been  used  in  ths 
previous  connections  of  chords,  ^he  fifth  goes  upwards  and  downwards, 
the  third  likewise,  sometimes  goes  a  degree  upwards,  and  sometimes  makes 
a  skip  of  a  third  downwards.  This  all  took  place  principally  in  reference 
to,  and  in  avoidance  of,  covered  fifths  and  octaves. 

Where  these  faulty  progressions  do  not  interfere,  the  third  especially, 
can  make  still  other  steps,  by  means  of  which  the  leading  of  the  voices 
often  becomes  more  independent  and  freer,  e.  g. 

a.  b.    not  good.  c. 


114. 


That  this  leading  is  also  possible  in  the  middle  voices,  if  the  position 
admits  of  it,  is  shown  at  c« 

The  leading  of  the  Soprano  at  h  is  not  good,  because  a  skip  of  an 
augmented  fourth  occurs  in  consequence. 

The  skip  from  the  fourth  to  the  seventh  degree,  (F-^B),  is  called  the 
Tritonus^  because  it  contains  three  whole  steps.  'More  of  this  sub- 
sequently. 

A  different  leading  of  the  fifth  is  possible  only  if  the'Bass  at  the  same 
time  deviates  from  the  above  progression,  which  is  that  of  a  fundamental ; 
as  in  general,  still  other  leading  of  the  voices  will  present  itself,  if  we 
search  out  other  than  the  chord-connections  hitherto  used. 

Tlie  Preparation  of  the  Seventh, 

Thus  far  the  progression  of  the  chords  of  the  seventh  has  been  spoken 
of,  but  nothing  has  been  said  of  their  introduction. 

The  harsh  eff'ect  of  the  entrance  of  many  dissonances^  and  particularly 
of  most  of  the  sevenths  in  the  secondary  chords  of  the  seventh^  rendera 
necessary  a  careful  introduction  of  them,  which  consists  in  their  pre' 
varation. 

A  tone  is  prepared,  if  it  exists  already  in  the  foregoing  chord  in  one 
AND  THE  SAME  VOICE,  and  as  harmonic  tone^  so  that  it  can  be  connected  by 
a  tie. 


MANUAL    OF    HARMONY. 


71 


Such  preparation  of  a  tone  is  contained  already  in  the  first  connections 
of  chords  previously  shown,  e.  g. 


115.   / 


^~X~\ 


mi 


(iimiiiir^y 


w 


It  can  be  said  here,  that  C  of  the  Soprano  in  the  second  chord  is  pre- 
pared by  the  G  of  the  first  chord ;  likewise  the  Gr  of  the  Alto  in  the 
Example  following. 

The  necessity  of  the  preparation  of  the  sevenths,  however,  does  not 
result  alone  from  the  harsh  effect  of  their  entrance  if  they  are  struck /re^, 
[enter  unprepared],  but  particularly  from  the  character  of  harmonic  con- 
nection and  binding  of  two  consecutive  chords,  which  is  especially 
characteristic  of  the  sevenths,  and  which,  without  the  preparation,  would 
not  appear.  ""^ — ■ ■ 

The  preparation  of  the  seventh  can  now  take  place  in  the  following 
manner : 


116. 


=d^J=4 


=d=F- 


^^sitss^mssm 


iig^ii;^ 


© — &— 


(2— 


^^^:E^M 


r 

7 


C:    V 


IV 


IV      IV 


IV       vii0.r   I 


In  all  these  Examples,  the  tone  which  is  connected  by  a  tie  with  the  fol- 
lowing like  tone,  forms  the  preparation  of  the  seventh. 

In  the  formation  of  such  preparation,  the  following  rules  are  to  be 
observed  : 

a.  The  preparation  takes  place  upon  the  unaccented  part  of  the 
measure  (arsis)  and  must  .  flk-  " 

b.  at  least,  he  of  as  long  duration  as  the  succeeeding  seventh  ;  it  can 
indeed  be  longer,  but  not  shorter,  e,  g. 


n 


Ur^-M^ 


72 


MANUAL    OF   HARMONY, 

not : 


iir. 


i; 


7 
K-« 1— 


^l^il 


::F 


Remark. — 7%e  preparation  of  the  sevenths  forms  one  of  the  most  important  parts  oi 
tlie  doctrine  of  harmony,  and  is  to  be  carried  tlirough  and  practiced  with  much  care, 
because  upon  it  rests  the  most  essential  part  of  the  inner  and  most  intimate  connection 
of  harmony. 

If  here  also  exceptions  in  the  practice  can  be  adduced,  we  may  still  again  be  re- 
minded, that  they  are  even  nothing  else  than  exceptions,  -which  prove  nothing  against  the 
importance  of  the  principle  of  harmonic  connection,  but  can  only  be  intended  and  Judged 
of  as  called  for  in  a  concrete  case  by  the  position  and  relations.     (Page  44 — Remark). 

These  exceptions  occur  mostly  with  the  minor  sevenths,  as  the  less  harsh,  as  those  of 
the  second  and  seventh  degree,  and  are  then  always  softened  by  good  leading  of  the 


An  especial  exception,  however,  to  the  necessary  preparation  is  formed 
by  the  seventh  of  the  dominant  chord,  also  called  the  essential  seventh. 
This  is  the  one,  which,  through  its  relation  to  the  tonic  triad,  enters  [with 
an  effect]  the  least  harsh  and  foreign  to  the  fundamental  key,  and  does  not 
require  preparation  in  all  cases. 

Of  its  farther  use  the  following  may  be  remarked 

The  dominant  seventh  does  not,  to  he  sure,  require  preparation,  yet  its 
y^ifree  entrance  demands  the  presence  of  the  fundamental  y  if  the  leading  of 
the  voices  is  to  be  pure  and  without  harshness. 


'7 


-,  ■     i — --1-  -^        J — J      -^ 


lis. 


Remark. — ^The  so-called  passing  sevenths,  which  of  course,  as  such,  cannot  be  pre- 
pared, conform  to  the  rules  of  the  passing  notes,  which  are  explained  later  Concerning 
the  passing  sevenths,  see  Chapter  XVIII. 

The  seventh  also  of  the  seventh  degree  in  major  and  minor  (m  the  last 
case,  the  chord  of  the  diminished  seventh),  by  reason  of  their  especial 
character,  do  not  by  any  means  always  require  a  preparation. 


^ 


MANUAL    OF   HARMONY, 


73 


Exercises, 
7  6 


6 

4  7 


119.  gJ^^^EfeEEfeEgEp^^ 


t^^ 


CZ^I 


:®=z^: 


=^=^ 


2. 

8           2 

6 

7 

L 

6 
5 

6 

6 

-G— 

6 
4 

7 

— 1~ 



-ff 

-^     \   / 

-(2 H-l 

-£::=t- 

-J- 

..C 

-F 

— 1 — 

f    . 

' 

~<9 — 

— fl- 

ril: 

3.  6 


m 


--tr- 


6 

4  7 


3E=S 


^li 


r  6 


6 

7  5 


6      6       7 


i^siiiiiiri^ii^j^jiiiiiE 


27ie  Connection  of  the  Cliords  of  the  Seventh  among  themselves. 

The  progression  or  resolution  of  the  chords  of  the  seventh,  took  place 
in  the  former  Examples,  always  through  the  triad  of  the  fourth  degree 
above,  or,  which  is  equivalent,  of  the  fifth  degree  below.  Instead  of  the 
triad,  a  chord  of  the  seventh  of  the  same  degree  can  also  follow. 

The  progression  of  the  voices  suffers  hereby  no  alteration,  only,  in  this 
case  the  third  of  the  -first  chord  of  the  seventh  will  serve  as  the  necessary 
preparation  of  the  following  seventh^  and  will  therefore  not  progress,  but 
remain  stationary,  e.  g. 


120. 


nm 


::5— : 


mmii 


C:       II 


IV 


Here  the  third  of  the  dominant  chord,  the  B,  forms  the  preparation  of 
the  following  seventh. 

The  peculiarity  in  this  connection  of  harmony  is,  that  in  one  of  tie 
chords  of  the  seventh,  the  fifth  will  always  be  wanting.  In  Example  120, 
the  fifth  of  the  first  chord  has  been  left  out.  If  several  chords  of  the 
seventh  succeed  each  other,  the  fifth  will  always  be  wanting  in  each 
alternate  chord. 


74 


M^ANWAL    4>F   M4MM9FT. 


121. 


VI  IVt'TII^^    llliy     VI17         Iliy     V» 


The  following  rule  may  therefore  apply  for  connections  of  harmony  of 
this  kind : 

If  two  or  more  chords  of  iJie  seventh  follow  each  other  in  the  funda- 
mental rosiTioN,  the  fifth  is  omitted  in  each  alternate  chord. 


4 

3         6 


Exercises, 

6 
6         5 


yE^ik^:EEEl 


1         7 


3e; 


2. 


7       7 


i^P^: 


EE 


4-        5 


S 


7       77       77366 

3=3 


E 


3 


2       6 

|3=i 


6       2       6       7       7 

-1- 


flil 


4. 


6 
6         5 


7       7 


91^; 


E 


:a= 


;^^ 


lom?'- 


3E 


E^J3 


1^^ 


Application  of  the  Secondary  Chords  of  the  Seventh  in  Minor, 

The  use  of  the  secondary  chords  of  the  seventh  in  minor  is  more  lim- 
ited. Many  of  them  show  themselves,  to  he  incapable,  or  indefinite  and 
ambiguous,  for  chord-connections  as  they  were  applied  in  major,  others 
form,  in  their  cadencing  progressions,  heavy,  unmelodic  steps  of  the  voices. 

A  chord  of  the  seventh  formed  as  the  first  degree  gives  it,  can  afford 
no  progression  analogous  to  the  above,  since  the  following  chord  connection 
is  not  conceivable. 


123. 


m 


VANUAL    OF    HARMONY. 


40 


Remark. — Even  if  with  the  above  combination  of   intervals,   progressions   can  be 
formed,  such  as  perhaps  : 


124. 


=g 


1 


i 


11       6 

still  this  -would  hardly  be  admissible  as  proof  that  we  have  in  this  a  progression  of  the 
chord  of  the  seventh  of  the  first  degree  in  minor. 

The  resolution  of  the  chord  of  the  second  degree  is  into  the  dominant^ 
and  is  very  frequently  used. 


125. 


i^i^l^i=l^^l 


=i=^: 


jsrz:. 


i^m. 


o 


iHII 

I. 

If 


IlO, 


A  progression  of  the  chord  of  the  seventh  of  the  third  degree  is  not 
impossible, 


136. 


il; 


I 


^^m 


II 


a:    IIIV    VI 


it  is  ambiguous,  however,  and  might  be  better  adapted  to  C  major  than  to 
A  minor.     (See  Altered  Chords). 

It  may  be  remarked  here,  in  addition,  that  the  ffth  in  this  chord,  as 
augmented  interval,  will  always  go  upward  one  degree. 

The  chords  of  the  fourth  and  sixth  degrees  are  unusual,  because  the 
leading  of  the  voices  in  their  resolution  becomes  inconvenient  and  un- 
melodic. 

y^      ^  good : 


1*7. 


a:    IV ^     vii'^ 


>^- 


7 


lE^^l^^mm 


-p 


p-- 


s^- 


■-P- 


:[[ 


76 


128. 


MANUAL    OF   HARMONY. 


g-f-i 


:    VIjT-    uo 


The  forced  character  of  most  of  the  above  progressions  is  unmistakable, 
and  prevents  their  frequent  use. 

The  seventh  degree  in  minor  brings  an  important  chord,  which  is  gener- 
ally known  under  the  name  of 

\  THE  «H#R1>  OF  THE  DIMINISHED  SEVENTH. 

A  resolution  of  this  chord  in  the  manner  of  all  the  rest  is  impossible, 
since  it  would  necessarily  result  in  the  triad  of  the  third  degree,  which  was 
already  represented  above  as  doubtful  and  ambiguous. 

Instead  of  this,  its  progression,  as  with  the  chord  of  the  seventh  of  the 
seventh  degree  in  major  (see  page  68),  is  based  upon  the  natural  progres- 
sion of  the  leading  tone^  upon  which  this  chord  rests : 


V 


129. 


Ei^?=l=!EE^:di 


c:  vu°i. 


As  the  fundamental  of  this  chord  (leading  tone),  progresses  a  half-step^ 
so  the  seventh  also  moves  a  half -step  downwards,  while  third  and  fifth  are 
led  just  as  regularly  as  with  the  other  chords  of  the  seventh ;  especially, 
however,  in  many  positions  (No.  130  a)  must  the  leading  of  the  third  be 
accurately  attended  to,  because  it  easily  produces  faulty  progression : 


not^ 


^      ^ 


130. 


Eil^^=fe 


iiill 


if^ 


•whereas-  the  position  at  h  and  c  gives  to  the  third  greater  freedom. 

Remark. — ^The  natural  progression  of  this  chord,  as  well  as  of  the  chord  of  the  seventh 
of  the  seventh  degree  in  major,  to  the  tonic,  has  occasioned  the  older  teachers  of  har- 
mony to  find  the  basis  of  it  in  the  dominant  harmony  of  the  seventh.  They  conceived 
of  thitf  chord  with  a  ninth  (major  or  minor)  added  to  it,  and  the  fundamental  omitted, 
whereby  arose  both  chords  of  the  seventh  degree. 

While  we  refer  to  that  which  is  said  later  (in  Chapter  IX.)  of  the  chord  of  the  ninth, 


MANUAL    OF   HARMONY. 


77 


fiQ  can  only  bring  forward  here  as  reason  for  the  view  offered,  that  this  assumption  of 
the  chQrd  of  the  ninth  is  needless  and  far-fetched,  and  that  for  practical  purposes,  th€ 
Bimplicitj  of  the  harmonic  system  has  been  preferred  to  the  more  excursive  explanation 
of  it.  * 

For  the  application  of  the  chord  of  the  diminished  seventh,  observe  in 
addition  the  following : 

The  diminished  seventh.^  as  the  mildest  of  all,  needs  no  preparation 
(See  page  72). 


131. 


m& 


3       6 


::r5t 


6       7 


Exercises, 

7 

%  6 


;if^ilililli 


2.    3 


7 

5« 


6  2      6      jar 


6  7 
4   « 


mm^ 


\=Si=f^Z±=^ZI^=^.. 


-^^^^ 


1=1 


7 

T=1: 


JBT      6 


*^?EiE^EEJEtEEH 


7  6       ^ 

«  4       2       6 


7 

7       « 


C^- 1 r 


9J.fe 


7 

If 


:F=t: 


-P—T- 


6  7 

4  Jf 


^1 


■F 


::1=' 


The  foregoing  and  all  previous  exercises  of  this  chapter,  which,  of  course, 
only  have  the  object  to  assist  us  in  learning  to  use  mechanically  the  chords 
thus  far  explained,  and  to  test  the  rules  and  remarks  laid  down,  have  some- 
thing inflexible  and  stiff  in  their  structure,  because  the  great  number  of 
chords  of  the  seventh  could  only  appear  here  in  the  fundamental  position^ 
and  because  the  introduction  of  many  of  them  upon  our  present  stand 
point,  which  did  not  allow  us  the  selection  of  other  means,  was  difficult,  and 
could  only  appear  forced. 

"What  follows  may  serve  as  explanation  of  them : 

The  fundamental  of  these  chords  of  the  seventh  makes  everywhere  the 
cadencing  skip  of  a  fourth  or  fifth,  as  is  to  be  seen  from  the  leading  of  the 
Bass,  only,  in  the  third  exercise  of  Nos.  122  and  131,  there  is  found,  seem- 
ingly, an  exception.  In  the  fourth  measure  of  the  third  exercise  of  No.  122, 
the  Bass  tone,  to  be  sure,  remains  stationary,  the  progression  of  the  funda- 
mental is,  however,  contained  in  a  perfectly  regular  manner  in  the  two 
chords:  A7,  D7.  The  Bass  tone  could  here  remain  stationary,  because 
we  have  already  learned  the  inversions  of  the  dominant  chord  of  the 
seventh,  and  can  therefore  use  them.     The  case  is  the  same  in  the  fifth 


78  MANUAL    OF   HARMONY. 

measure  of  the   third  exercise  of  No.  131,  where  the  progression  of  the 
fundamental  A7-D  takes  place  with  a  stationary  Bass. 

In  the  second  Exercise  of  No.  !P81  the  chord  of  the  seventh  of  the  third 
degree  in  minor  is  used,  and,  it  may  be  assumed,  that  with  this  introduction 
it  will  not  appear  unnatural  and  harsh. 


CHAPTER    VII 


The  Inversions  of  the  Secondary  Chords  of  the  Seventh. 

Through  the  inversions  of  the  secondary  chords  of  the  seventh  the  same 
derived  chords  arise,  which  have  already  shown  themselves  before  with  the 
dominant  seventh,  viz.,  the  chord  of  the  sixth  and  fifth,  of  the  sixth, 
fourth  and  third,  and  of  the  second. 

The  variousness  of  the  third,  fifth  and  seventh  of  the  fundamental  har- 
mony occasions  no  alteration  in  the  treatment  of  the  inversions.  For 
although  the  major  seventh  changes,  through  inversion,  into  a  minor 
second,  and  the  diminished  into  an  augmented,  still  its  progression  will 
ensue  in  the  same  manner  as  has  already  been  explained  above. 


132. 


There  is  need  of  no  new  rule  for  the  progression  of  all  these  chords  of 
the  seventh.  Only,  that  of  the  seventh  degree  in  major  and  minor 
requires,  as  was  before  remarked,  a  little  caution  on  account  of  the  easily 
occurring  open  fifths. 

Somewhat  more  concerning  their  treatment  may  follow  here. 

Progression  of  the  Chord  of  the  Seventh  of  the  Seventh  Degree  in 
Major. 

6  4  6 

6_ 6 not:        3 6^ 2 4 


All  these  inversions  of  the  chord  may  be  used,  only  the  last,  the  chorrl 
of  the  second,  will  most  seldom  be  in  place,  since  the  resolution  into  the 


MANUAL    OF    HARMONY. 


79 


chord  of  the  sixth  and  fourth  could  only  occur  in  rare  cases,  and  at  most 
as  passing  chord. 

We  must  not  allow  ourselves  to  be  misled  in  respect  to  their  usefulness, 
by  the  crowded  position  in  which  these  chords  are  exhibited  in  No. 
13S.  It  is  only  important,  as  was  mentioned  before,  whether  the  seventh 
comes  to  lie  above  or  helow  the  fundamental  (see  page  69),  and  positions 
of  the  chords  of  the  sixth  and  fifth,  and  of  the  fourth  and  third  of  the 
following  sort, 


134. 


^-=. 


4  ^       * 

3         6 


appear  more  satisfying,  because  the  seventh  lies  above  the  fundamental. 

The  chord  of  the  diminished  seventh  requires  a  manner  of  progression 
similar  to  the  foregoing  e.  g. 


135. 


5        6       <w;     5         6  3         6 


4 

2J 


~ii^=3^ 


:z^: 


a^[[ 


That  here  likewise  the  third  inversion,  the  chord  of  the  second,  will  be 
that  least  adapted  for  use,  is  shown  by  the  unsatisfying  resolution  into  the 
chord  of  the  sixth  and  fourth,  a  chord  which  always  requires  a  careful 
treatment,  concerning  which  chord,  what  is  necessary  follows  later. 

That  successions  of  fifths,  which  arise  through  resolution  of  the  chords 
of  the  sixth  and  fifth,  and  of  the  fourth  and  third,  in  this  manner : 


136. 


are  to  be  regarded  as  faulty,  has  been  already  mentioned  above,  (page  76). 
Concerning  the  succession  of  this  sort  of  fifths,  compare  also  page  29,  Nos. 
16, 17,  and  18. 

With  this  exceedingly  pliant  chord,  the  position  of  the  fundamental  as 
respects  the  seventh  produces  no  such  material  difference,  as  with  the  chord 
of  the  seventh  degree  in  major ;  the  seventh  can  lie  above  or  below  the 
fundamental,  the  similarity  of  sound  of  the  augmented  second  to  the 
minor  third,  will  always  impart  much  mildness  to  the  chord  and  cause  tho 
former  only  to  be  felt  as  such  in  reference  to  the  key. 


80 


MANUAL     OF   HARMONY. 

Exercises, 

G  6 

6       6  5  5  6 


«..  §-E^EE;|Epi^|E^|E^|^EE^|Ef^Eg^|E 


2.    3 


4 

3     7 


l>iE^i^E 


gi^i^g^tlii#i^i 


t=t^ 


6 
2    5 


6 
6         5 


2     6 


2     6 


9Je$5^.= 


*§E^£ 


*EE^EEEtE:HEEEEfe 


9=i^E^^^^SE 


2    6       7  3      6     6 

:qz:q=:p= 


6 
6         5 


— (9 i 


Z5t?: 


6 
6     5 


6                        6 
6.         3^2    6       2    6         4    2        6    5       7    7 


-J^ZL^l 


6 

6     « 


6  jar 


f  6 

7    7        3    6        5     « 


^^gfifei^i 


§iE!$; 


-S^/2- 


Ei 


f 

8.       3        2     7  6  7         3    6 


6 

5     8 


gfE^Egg^l^g^gE^ii 


:ip=t:i 


f    6 


7    6 

7       5     6 


6  7  6      6'7 

«       7    7         «  4      4S 


9iiE^ 


-^ls-^|illliEL=|=|^= 


^E; 


10. 


^  4 

66       73«2      6)8- 


6 
6      4     « 


■?^ 


— (^ .-«.. 


SEE 


t=t 


iSPi^i: 


^ 


\ 


MANUAL    OF    HARMONY.  gl 


CHAPTER  VIII. 

The  Cliords  of  the  Seventh  in  connection  with  Chords  of  the 
various  tone-degrees  other  than  those  thus  far  used.  Decep- 
tive Cadences. 

The  known  rule,  that  the  seventh  must,  in  the  resolution,  progress  one 
degree  downwards,  verifies  itself,  to  be  sure,  completely,  in  the  connections 
of  chords  previously  shown,  but  it  has  as  little  positive  authority  as  any 
thing  else  which,  under  other  conditions,  and  in  the  great  variousness  of 
chord  connections,  is  subject  to  necessary  alterations. 

In  the  movement  of  the  seventh  or  of  its  inversion,  the  second,  every- 
thing depends  upon  the  progression  of  the  fundamental.  If  this  is  of 
such  sort,  as  in  all  the  cases  hitherto  shown,  that  without  the  downward 
progression  of  the  seventh  no  intelligible  and  satisfying  result  would  be 
produced,  then  also  the  above  rule  will  have  full  application. 

The  progression  of  the  fundamental,  however,  can  entirely  set  aside  this 
direction  of  the  seventh ;  it  can  either  remain  stationary  or  even  pro- 
gress upwards,  e.  g. 


13§. 


7  f 

^  L^    3 


^Mm^mm 


This  leads  us  to  the  possibility  of  connecting  the  chords  of  the  seventh 
with  chords  of  tone-degrees,  other  than  those  hitherto  used.  A  few  known 
kinds  of  chord-connections  now  follow  with  remarks,  in  order  to  be  abley 
in  attempts  at  new  formations  of  the  kind,  to  proceed  according  to  critiedt 
principles. 

We  begin  with  the  dominant  chord  of  the  seventh. 

It  has  been  mentioned  before,  that  the  resolution  of  the  chords  of  the- 
seventh  in  the  manner  hitherto  used  is  called  cadence,  and  that  of  the* 
dominant  chord  of  the  seventh  closing  cadence. 

If  any  chord  other  than  the  tonic  triad  follows  the  dominant  chord  ol 
the  seventh,  the  natural  inclination  to  a  close  is  either  delayed  or  entirely 
set  aside. 

The  expectation  of  the  natural  succession  experiences  hereby  a  disap- 
pointment, and  for  this  reason  these  connections  of  chords  are  called 

DECEPTIVE    CADENCES. 
Deceptive  cadences  arise  thus  everywhere,  where  the  progression  of  tha 
dominant  chord  of  the  seventh  does  not  result  in  the  tonic  triad,  but  leads 
♦:o  other  chords. 


82 


MANUAL    OF   HARMONY. 


Some  varieties  of  them  will  next  be  explained. 

1.  The  connection  of  the  dominant  chord  of  the  seventh  with  triads^ 
other  than  that  of  the  tonic,  ivith  a  progression  of  the  seventh  hy  de- 
grees  downwards. 
y  a*     Connection  with  the  sixth  degree. 

In  Major.  Jn  Minor.  3    ^  i^ 

139.  ^==|S^f z1==g£^£Ez^^E^3zg^r^g^^^ 

C:    V^      Ti  0'   ■2?!-^        "^L-^    x:  V^^     TI  


This  chord-connection  (deceptive  cadence)  occurs  very  frequently. 
The  effect  of  this  progression  is  not  so  decided  with  the  inversions  of 
the  chord  of  the  seventh,  and  is. therefore  more  rare  : 


140. 


In  Major. 
6  6 


In  Minor. 
6 
5         6 

■G- 


"G^  ^^■^'^'Z 1 1 ^ 1 ?5" r^: — &' rr 


r^^. 


VI 


y  1>.     Connection  with  the  third  degree. 
7  _       6 


letter  position 
7  6 


141. 


Remark. — Tlie  attempts  with  the  inversions  of  the  chord  are  omitted  here  and  in  what 
follows ;  they  are  easily  made. 

This  progression  becomes  more  decided  under  the  application  of  modu- 
lation : 


142.  iL=i 


6 

g? r 


=i^i=yi=z|= 


C:    Vt  a:V 


— j:. 


I 


^ 


The  connection  with  the  triad  of  the  third  degree  is  also  possible  in 
minor,  but  this  as  dissonant  chord  (through  the  augmented  fifth)  will  make 
A  farther  succession  necessary. 


7  6 

t  - 


143.  itz 


wimmM^ 


325?: 


"m 


III'       VI 


2.  The  connection  with  triads,  the  seventh  remaining  stationary. 


MANUAL    OF   HARMONY. 
a«      With  the  second  degree, 

y  1  i4.  ^'=\ 


83 


not: 


6 


impracticable  in  Minor, 


%=iH^M^i=^=h 


-t. 


I 


C:     V 


a:    V-y    iio 


\     !>•      TFii^^  the  fourth  degree. 

In  Major : 


*^'  ^=§=^^-]=g}:^^]=| 


/«.  Minor  : 

6  u         6 


C:     V 


IV 


Tsr    -^ 


A :    V  IT     IV 


The  connection  of  the  dominant  chord  of  the  seventh  with  harmonies 
of  the  seventh  of  other  degrees  beside  those  before  used,  is  likewise  pos- 
sible.    A  few  of  them  follow  here  : 


146, 


I  I, 


Gth  Degree 
2 


Sd  Degree , 
6 
5 


5 J^ 


Minor  :         Sd  Degree, 


C:      Vh 


— 1^ 


~g: 


V^    a:Vy       a:  V^       IIF-y     VI 


we  modulate  into  other  keys,  the   possibility  of  new  connections 
extends  itself  greatly,  e.  g. 
f.    a*     With  a  doivnward  progression  of  the  seventh. 


not. 


14T, 


hett^r : 


C:    V-yD:V. 


^^^^^^mmt^m^ 


C:  V^  Brvno*-  a:  Vo-  F;  V.y    ArVo-Gtviio 


I*.     The  seventh  remaining  stationary. 


C:    VyE|j:Y-j-     C:  Y,y^}:Y<y      a:  V^  C:  Viy       ArV^GrVY 

3.  The  connection  of  the  chords  through  an  upward  progression  of  the 
seventh. 

This  case  can  occur  with  the  common  cadence  (V — I). 

a*      With  an  exchange  of  the  progression  of  variou*  voices- 


84 


s 


149. 


MANUAL    OF   HARMONY. 


not :      ^ 


7       6 


F-^-^o F=^"^~f" 


ffl:^^__: 


i 


Tiarougli  the  step  of  a  third,  of  the  Bass,  the  downward  progression  of 
the  seventh  becomes  impossible,  since  the  covered  octave  occurring  thereby 


ISO. 


g^g? 


1 


1 


is  in  any  case  faulty. 

In  the  remaining  voices  this  progression  of  the  fundamental  cannot  bo 
introduced. 


151. 


i 


^-^-fii- 


-ffl-=^ 


-J?— 


-o  ^^  g 


^^mi 


^ 


G- 


=:?Eb?^:^l 


X 


All  these  Examples  are  faulty. 

The  fundamental  remaining  stationary  : 

not : 


153. 


— ci — 6, — a. 


4 

:5?zz3<iz7.g: 


-O^"^ 


-©=^Sk=;^- 


;^ 


•*■    ^    ^ 


-jr?r^ s 


l=^^=|3=^^l 


C:    I       Vp 


The  fundamental  serves  here  as  so-called  stationary  voice.  (See  later : 
Organ  point).  It  must  however  lie  at  a  distance  from  the  seventh,  and 
the  following  progression  would  be  faulty : 


153. 


MANUAL    OF    HARMONY. 


Through  chromatic  alteration  and  with  modulation. 


154. 


f 

a  3 

'~0~ 


C:  V-r  G:  V. 


*E 


enharmonic  : 


— _. — ^ tt,5, . — I 


«' 


-2;- 


C:  V, 


G:  V. 


V.y    b:  vuO^      C:  V^   H'  V^ 


d.     Through  contrary  motion  of  the  Bass  tvith  modvlation  into  other 
keys. 

155. 


_   a ^— \iZd , -:;,,-= ^ , ^-— C< 1  1 


C:  V-y  d:  V^       C:  V^  bIj:  viio,y    a:  V^  d:  viiOiy      C:  V^  F:  V^ 


5ee  above,  No.  149.) 


The  foregoing  catalogue  of  chord-connections  gives  only  an  indication 
of  possible  combinations.  The  object  of  them  was  to  call  attention  to 
the  manifoldness  of  harmonic  progression  and  its  capability  for  con- 
Btruction. 

Concerning  the  worth  of  these  and  similar  chord-combinations,  criticism 
can  only  decide  in  especial  cases,  since  their  right  use  becomes  possible 
only  with  a  proper  attention  to  their  introduction,  their  succession,  their 
rythmical  weight ;  in  short,  their  whole  situation. 

The  particular  character  of  a  piece  of  music,  the  peculiarly  formed 
leading  of  the  voices  through  the  application  of  a  motive  or  thought,  and 
the  like,  can  lead  to  such  combinations  of  harmony ;  to  apply  them,  however, 
upon  speculation,  to  produce  new  and  strange  forms  in  any  case,  in  order 
to  appear  original,  would  probably  in  few  instances  so  succeed,  that  the 
intention  would  not  be  apparent. 


Exercises, 


A 


1.       3 


8  7 


.5«.  iii.iiii^^l?il 


7     7 


4    6 
3    4 


6    6 
6    4 


2     6       6     7 


ilE^fel^ll^i^ 


_„_i:=i!=3i|r©Tz:i: 


86 


MANUAL    OF   HARMONY. 


iS 


4 

7  3 


6 

4  7 


S^J^itlpi^- 


:t: 


±z:t 


4. 


5    6 


iL?:^£( 


6    6 
5    5 


6 
6     5 


6         6 


(5»- 

7     7 


;EEEEEi; 


5.  open  position.  3     6 


6     7 


^E^fefe£^=£^=il 


liE^^^lE^ 


-»--(=- 


;iEEEE 


;ee?e^ee 


6 

4  7 


i 


^M 


6.       3 


6  7 

41 


6 


4     6 
3     4 


6 
2       5 


7 

7     Jf 


^Eli^^§^^^i^^i^^E^i= 


6  7 

4  «       6    J3r 


6    4 
4    3 


6     6 


6  7 

4  « 


§iE^Ei 


SEEEEESrlSEEEEEEESEFS^EfE 


9Jf^j 


ifelEEE 


6 

5  7 

-stE'?: 


6 
4  7 


^3: 


;i^i^[|^E 


Remark. — ^The  opcw  position  of  the  5th  exercise  has  reference  to  a  leading  of  the  voices 
adduced  page  84 ;  farther  on,  it  can  be  abandoned  again. 

The  Secondary  Harmonies  of  the  Seventh  Connected  ivith  Chords 
of  other  Tone-Degrees  or  Keys, 

A  few  more  connections  of  chords  with  secondary  chords  of  the  seventh 
may  here  follow.  To  adduce  all  cases  of  the  kind  would  be  as  impossible 
as  it  would  be  without  object. 

SI*      With  regular  progression  of  the  seventh. 


15T. 


C:  Iliy 


:-=l-l-fe 


^s^^i^M%m^\mm\ 


not: 


-^—iP 

II Y  KrVY    C:  iiipy     IV 

hetter: 


iiw  F:V,r      C:  IVyG:V- 


t^f^mm^m^mm^i 


a:  no-r      HI' 


.f 


VlrGcV-y    A:\n°y   p:  viio* 


b*     With  free  progression  of  the  seventh. 


MANUAL    OF    HARMONY.  87 

not : 

*^  -^  isr  ■O'  ^^ 

C:  11^  G:  V-y    C:  ii-j-  c:  viio^  C:  iiy  a  :  V^       C:  ii^y    i>:  vn^iy 

Remark. — The  reason  why  the  last  exa-mple  is  not  good,  lies  m  the  so-called  cros»» 
relation  therein  found,  the  explanation  of  which  follows  later. 

C.     The  seventh  remaining  stationary. 

h.  c.  d.  6  6 


C:    iiy       IV  11^        Yi  11^         I    -  ,-11^         I  V 

The  last  chord-succession  is  often  used.  It  forms  a  ^elay  of  the  caden- 
cing  progression  of  the  second  degree  to  the  fifth,  through  the  inserted 
chord  of  the  sixth  and  fourth  of  the  tonic  triad.  Its  chord  of  the  sixth 
also  often  appears  between  this  chord  and  its  resolution,  as  in  Example  €• 

The  chord  of  the  diminished  seventh  is  often  used  in  like  manner : 


160. 


G5  0  G 

7'2         4  5i?         4 


mmmmmiw^s^i 


r.    vuo^  C:  I 


TV  77 


Here  also  the  natural  progression  is  only  delayed  through  the  chord  of 
the  sixth  and  fourth. 

The  mechanical  combination  of  such  chord-successions  may  be  left  to 
personal  practice  and  investigation.  The  advantage  of  it  will  lie  in  the 
insight  gained  into  the  relations  of  chords,  and  therefore  is  not  to  be 
esteemed  so  insignificant  as  it  might  at  first  appear ;  this  [practice]  will, 
in  fact,  stand  in  about  the  same  relation  to  composition,  as  the  technical 
studies  and  preparatory  exercises,  to  the  practical  bringing  out  and  repre- 
sentation of  musical  works.  Both  produce  aptness  and  skill,  educate  the 
powers,  and  render  intellectual  productions  possible. 

It  may  here  only  be  remarked  in  addition,  that  the  relation  of  the 
seventh  to  the  fundamental  and  its  progression  must  always  be  regarded 
as  the  criterion  of  the  above  combination.  If  this  is  pure  and  the  remain- 
ing voices  form  none  of  the  before  mentioned  faults,  then  the  chord- 
combination  can  be  used  for  particular  cases. 


Eijcercises, 

J}^ 5 C_ 

101." 


7 
5  6 


gil^E^i^fEz-EE^^^^SEEIgblr^-pI-l 


88 


MANUAL    OF    HARMONY. 


6 

5       6 


7  6 


§;eb; 


g 


T 


:F= 


eeefeE: 


2       6 

=t=::3: 


i^E 


4      7 
7  3      6  6 


6      6 
6     4      5 


i&l^l^i=l^ 


m=^ 


iss 


6      6 
5      4 


6       6 


6 
7        4      7 

T-G- 


6         6  7 

7         6       5         4  S 


5.      3 


H=5-E 


■«  — 


trztis^ 


6.     3 

-Q- 


7 
5$    6 


js- 


6  7 

4$ 


Xg^E^EEE^ 


:=l: 


?i£ 


^SEgi^iEEE^^^Ii^Ji 


r 


7.     6 


s 


6^^2«    «     2       6 


J9r      6 
7       5       4       2 


T-« — r-T-^ — *—» 


87 

6    5 


lgi-lE^E=il^i 


f     6 


4      6 
3       5 


6  7 
4  # 


9-p|E^_^|-^^^^^^3||3^1^_E:3i^ 


1 


Remark. — ^Many  of  the  cases  above  adduced  could  not  be  taken  up  in  these  exercises, 
l>ecau8e  they  are  based  upon  modulation,  which  is  not  particularly  explained  until  latei-. 
(The  sixth  exercise  makes  a  little  application  of  modulation.)  Many  of  the  above  Ex- 
amples would  also  have  become  smoother  and  less  stiff  and  strange,  by  the  application 
of  modulation. 


CHAPTER  IX. 

On  Chords  of  the  Ninth,  Eleventh  and  TTiirteenth, 

In  most  text-books  are  found  extended  discussions  respecting  these  cbord- 
formations. 

The  views  which  can  be  plausibly  maintained  respecting  them  are  vari- 
ous, and  will  lead  to  the  same  practical  result.     We  can  assume 


MANUAL    OF   HARMONY. 


Either,  that  this  combination  of  intervals  is  to  be  regarded  and  treated 
fts  real  chords  ; 

Or,  that  they,  as  unessential  chord-formations,  either  belong  to  the  sw£- 
pensions,  or  arise  accidentally  on  account  of  a  voice  remaining  stationary. 

In  the  first  case,  the  explanation  of  their  use,  especially  through  their 
inversions,  becomes  very  extended ;  and  also  obscure,  (since  in  the  four- 
voiced  movement  one  or  more  of  their  tones  or  intervals  must  be  omitted) 
because  they  are  then  easily  mistaken  for  other  chords. 

In  the  second  case  their  explanation  becomes  much  more  simple. 

Remark. — The  ehoi'ds  of  the  ninth,  as  -vrell  as  those  afterwards  named,  are  a  relio 
of  the  old  so-called  thorough-bass  doctrine,  which  was  fond  of  conceiving  of  every 
combination  of  tones,  however  accidental  it  might  be,  as  an  especial  chord  and  taught 
its  treatment,  without  arranging  the  many  chance  chord-phenomena  under  a  definite 
system,  and  thereby  made  the  whole  doctrine  of  harmony  much  more  difficult  and 
diffuse. 

^  Without  being  able  here  to  enter  into  the  theoretic  reasons  which  class 
this  kind  of  formations  with  the  accidental  ones,  the  possible  simplificatiofi 
of  the  harmonic  system ^lihowi  real  practical  disadvantages,  determines  us 
at  once  to  the  last  view.     (More  respecting  this  in  Part  II.) 

In  order  to  gain  a  clear  view,  the  formation  of  these  unessential  chore's 
will  be  shown,  and  remarks  added. 

If  we  add  a  ninth  to  the  dominant  chord  of  the  seventh,  a  chord  arises, 
which  is  known  under  the  name  of  the  dominant  chord  of  the  seventh  and 
ninth. 

In  Major  :        In  Minor : 


162. 


t^ 


In  major  we  find  the  major,  in  minor  the  minor  ninth. 

This  chord  is  used  in  the  pure  harmonic  structure,  as  in  similar  relations 
the  dominant  chord  of  the  seventh  itself,  with  preparation  of  the  ninth  or 
of  the  fundamental ;  and  cases  of  the  following  sort,  where  loth  tones 
enter  free 


163. 


^m 


^ 


i 


are  to  be  censured  on  account  of  their  stiflFness  and  want  of  connection. 
This  preparation  can  be  effected  thus : 


90 


MA^'UAL    OF   HARMONY. 


betUr: 


164. 


1^1 


t=iE:Lzz:t:zidzit:=:bt:zz:liz:E-'g-Hbg: :: 


pTE^Ep^E^EpEp;EE|; 


;ee 


--=b: 


a 


mi 


How  far  the  first  examples  are  to  be  reckoned  as  belonging  to  the  sus- 
pensions, and  the  last  to  other  accidental  chord -formations,  cannot  be 
explained  until  later,  in  Part  II. 

Remark. — From  the  chord  of  the  ninth  in  major  thej  derive  the  chord  of  the  seventh 
of  the  seventh  degree,  -which  we  have  treated  of  fully  hefore  ;  likewise  the  chord  of  the 
diminished  seventh  from  the  chord  of  the  ninth  ia  minor,  in  order  to  be  able  to  form 
their  cadeneing  progression  iu  a  manner  analogous  to  that  of  the  other  chords  of  the 
seventh,  since  it  is  said,  that  these  chords  are  themselves  dominant  chords  of  the  seventh, 
to  which  the  ninth  is  added,  and  the  fundamental  of  which  is  omitted,  e.  g. 


165. 


Through  this  arises,  with  the  first,  the  complication  that  we  must  accept  of  two  chords 
of  the  seventh  of  the  seventh  degree  ia  major ;  one,  the  natural  cadence  of  which  is  the 
following : 


166. 


the  other  as  derived  from  the  dominant  chord  of  the  seventh,  while  it  remains  the  sim- 
plest way  to  refer  to  the  character  of  the  leading  tone  upon  which  the  above  chords 
rest. 

That  many  musical  text-books  accept  also  of  secondary  chords  of  the 
seventh  and  ninths  renders  the  explanation  of  many  harmonic  formations 
still  more  complicated,  and  is  just  as  little  necessary,  since  none  of  these 
tones  are  to  be  introduced  without  preparation,  whereby,  in  their  whole 
treatment  and  succession,  they  differ  in  no  respect  from  the  suspensions. 

That  which,  according  to  the  practice,  as  well  as  according  to  a  more 
simplified  theory,  applies  to  the  chords  of  the  ninth,  will  apply  in  still 
greater  measure  to  the  chords  of  the  eleventh  and  those  of  the  thirteenth. 

The  strange  and  frightful  form  of  these  chords  is  the  following : 


167. 


MANUAL    OF   HARMONY. 


91 


In  the  pure  four-voiced  movement  they  can,  of  course,  never  be  applied, 
since,  through  the  necessary  omission  of  many  intervals,  they  will  appear 
simply  as  suspensions,  e.  g.^ 


16S. 


and  even  in  the  polyphonic  movement  they  will  not  distinguish  themselves 
at  all,  in  their  character,  from  the  suspensions ;  in  the  more  free  stylo, 
where  they  also  appear  without  preparation,  they  can  be  regarded  as 
changing  notes. 


M--^^ 


^,Zy 


CHAPTEK    X. 


Chromatic  Alteration  of  the  Fundamental  Harinonies,    Altered 

Chords, 

The  chromatic  alteration  of  one  or  several  intervals  of  the  fundamental 
harmonies  has  a  double  effect : 
Either  it  produces  a  modulation, 

Or,  it  gives  to  the  chord  a  new  formation  not  hitherto  used  hy  us. 
If,  for  example,  the  major  triad  is  altered  in  this  manner,  there  arise 
a.     Modulations : 


169. 


gH§j^^Ep=|5|^|E^|H^E^|=pg§^ 


Through  Cjf,  the  diminished  triad  of  the  seventh  degree  in  D  major  or 
D  minor,  or  the  second  degree  in  B  minor ; 

Through  Et?,  the  C  minor — triad ; 

Through  El?  and  Gi?,  the  diminished  triad  of  the  seventh  degree  of  D!? 
major  and  minor,  or  the  second  degree  of  Bj?  minor. 

The  last  two  alterations  are  mere  transpositions  of  the  same  chord  into 
other  keys,  viz.,  Cb  major  and  CJj  major. 

!>•    New  Formations: 

1.0.  mEm^i='^i^^=i^mi^^i 

Of  these,  the  formations  a^  &,  <?^  j^  can  indeed  be  produced  accident" 


92 


MANUAL    OF   HARMONY. 


ally  through  hy-tones  (passing  tones) ;  they  have,  however,  nff  harmonic 
value. 

It  is  otherwise  with  the  formations  at  c  and  e^  which  maintain  harmonid 
(accordliche)  significance. 

The  first  form  of  the  triad  (c)  is  known  under  the  name  of 
THE    AUGMENTED    TRIAD. 

This  chord  was  found  before  upon  the  third  degree  in  minor  (see  page 
43) ;  it  appears  seldom,  however,  in  this  situation,  as  has  been  previously 
mentioned,  but  more  often  as  triad  of  the  first,  fourth  and  fifth  degrees 
in  major,  with  chromatically  raised  fifth. 

Its  origin  from  the  passing  tone  (G{()  to  the  next  following  (A)  is  easy  of 
explanation,  as  also  its  progression,  which  is  determined  through  this  tone 
(Gjf)  as  augmented  interval. 


171, 


i^=:8: 


^^^ 


&C 


1 


The  inversions  of  this  chord  can  also  be  used. 


172. 


pS^g^Ei=^^ 


C:    I         IV  VI  IV       viio 

Although  these  chords  appeared  for  the  most  part  in  passing,  or  through 
preparation  of  the  augmented  fourth,  they  can  also  enter  free  in  case  of  a 
rapid  change  of  the  harmony : 

1.11,1 

^— |— ^— r — r-^ ^^ 


173. 


313 


^n^^is 


To  the  augmented  triad  can  be  added  not  only  the  dominant  seventh^ 
which  occurs  most  frequently,  but  also  the  major  seventh  of  the  first  and 
fourth  degrees. 

a*     The  augmented  triad  in  connection  with  the  dominant  seventh  : 


174. 


MANUAL    OF    HARMONY. 


1).     In  connection  with  the  seventh  of  the  first  degree : 


■#=- 


-h- 


175. 


C:     I 


IV 


TAe  addition  of  the  seventh  to  the  augmented  triad  of  the  fourth 

is  very  rare : 

6  ^ 

7  5  4  4 

6«  I  3       6  2       6 


176. 


^ — ^ — H — P~P — r — ^~^ — r — p~^ 1 


^_i-_-f._,._fe_^ 


EteE!^^=E?EE[l 


C:    IV-yviiO 


In  all  these  chord-connections  thus  far,  the  cadencing  Bass  progres- 
sion, [e.  g.,  Y-I  I-IV)  has  been  used :  some  examples,  however,  may  show, 
that  these  chords  treated  of  can  also  be  used  with  chords  of  other  degrees, 
and  a  various  progression  of  the  Bass. 


177, 


7 
5$    6 


7 
5$   6 


6     - 

4      3 

6     9      8 


6 

«^  3  b 


ife=pi^ii-^i^plteE^^ 


=:g-g_=q=:Jz:S2 


i^^^i 


:i^ 


i: 


C:    V.y    ^11 

7 

5« 


V^- a:V       C:  V^  d:viio 


C:  Vry  o:  viio 


^— gg- 


5  5  7         6  6  I      « 


a^^=j^Pg^ll|[; 


C:  V^-  e:  V> 


C:  m      Ir  »:  V     C:  iii 


Q:V. 


These  occasionally  strange  and  rough  sounding  harmonic  combinations 
acquire  significance  only  through  the  situation  which  they  occupy,  and 
especially,  if  in  a  certain  degree  an  inner  necessity  leads  to  them. 

If  it  is  the  province  of  a  text-book  to  call  attention  to  the  possibility  of 
such  harmonic  formations,  it  is  also  its  duty  to  warn  the  beginner  against 
over  valuing  the  ivorth  of  such  stimulants ;  to  advise  him  in  general,  not 


94 


MANUAL    OF   HARMONY, 


io  occupy  himself  with  such  things  and  speculations,  until  he  is  fully 
versed  in  the  treatment  of  the  simplest  harmonies  of  the  simple  pure 
harmonic  structure.  A  too  early  occupation  therewith,  and  intentional 
seeking  out  of  especial  effects  will  render  difficult,  and  probably  impossible 
the  clear  view,  and  the  insight  into  the  simple,  fundamental  features  of 
harmony,  and  turn  away  the  sense  from  the  chief  thing  to  secondary 
matters. 


Exercises, 


1.      5  5$     5  5$     3  6 


17H 


.  ^E&EEE: 


-© 


I 


I 


3    2 


6 
6jf 


5  5S     6  2 


6 

4  7 


ii^EETi^fe"El=E^rEl^«^^^l^l=i 


6  6$ 
5  4 
2 


6     7 


m^=^. 


::iipz 


6  6 

6  4  7 

IE33EI^E^ 


6      7    7 


1 


-^=^- 


i^i 


3  5t 


7  6 
5  — 


ggE^lE^lE^I 


6 


NB. 
3  5t 


6        6 


:3= 


-si g-+ 


G 
5 

T-T- 


lIZITZI 


iiy 


Remark. — In  the  fourth  exercise  the  augmented  fifth  has  been  used,  even  with  the 
minor  triad  of  the  second  degree  (at  NB),  which  in  this  connection  does  not  sound  un- 
natural. This  would  correspond  to  the  formation/  before  in  Example  N"o.  170.  It 
is  seen  from  this,  that  with  a  natural  leading  of  the  voices,  many  new  chord-formations 
can  be  gained. 


■■=m-- 


—   (which  also  occurs 


From  the  formation  e  of  example  170  : 


under  the  name,  double  diminished  triad) ,  arises  a  harmony  which  is  much 
used,  viz : 

THE  AUGMEISTED  CHORD  OF  THE  SIXTH. 
The  first  inversion  of  the  above  chord  gives  it : 


179. 


According  to  its  progression,  which  is  determined  by  the  augmented 
sixths  the  original  chord  belongs  here  to  Gr  minor,  the  fourth  degree  of 
which,  C  minor,  with  a  raising  of  the  fundamental,  goes  to  the  fifth  degree. 

Wherever  this  chord  appears  with  its  natural  progression,  shown  above, 


MANUAL    OF    HARMONY.  95 

Example  No.  179,  the  last  chord  shows  itself  as  dominant.  The 
proof  of  this  lies  in  a  few  harmonies  formed  like  the  augmented  chord  of 
the  sixth,  the  augmented  chord  of  the  sixth,  fourth  and  third,  and  the 
augmented  chord  of  the  sixth  and  ffth,  the  explanation  of  the  basis  ot" 
which  follows  farther  on. 

Remark. — The  relation,  in  which  the  augmented  chord  of  the  sixth  stands  to  the  just 
noticed  chords,  allows  its  origin  to  be  referi'ed  to  the  same  source.    See  later. 

The  augmented  chord  of  the  sixth  has  the  peculiarity,  that  its  third 
only  (the  fifth  of  the  original  chord)  can  be  doubled  in  the  four-voiced 
movement : 


I§0. 


Of  the  remaining  positions  of  the  original  chord  (the  so-called  double 
diminished  triad),  the  first  (fundamental  position)  can  be  used  three- 
voiced,  but  very  seldom,  the  third  (second  inversion),  also  four-voiced,  only, 
however,  in  a  very  open  position. 

a,  b.    not :  not :  'better : 


Remark. — The  chromatic  alteration  of  an  mterval  of  the  minor  triad  is  already  con- 
tained in  the  formations  of  Nos.  169  and  170,  and  thus  needs  no  farther  investigation. 
Just  so  the  chromatic  alteration  of  an  interval  of  the  diminished  triad  will  either  pro- 
duce major,  or  minor  triads,  or  formations  which  are  already  found  above  in  the  place 
referred  to. 

Thus  the  formation  of  the  triad  in  No.  IVO,  d  will  be  like  the  following,  which  ig 
found  in  C  major : 

letter  in  open  position  : 


^.,.^m^E^^^^ 


C:    vuo  ^ 

This  chord  bears,  in  many  text-books,  the  name  :  harsh  diminished  triad,  (hart  ver- 
minderter  Dreiklang). 

The  like  chords,  if  they  may  be  so  called,  appear  generally  only  accidentally,  in  pass- 
ing, and  their  progression  proceeds  in  accordance  with  their  intervals,  that  is,  augmented 
intervals  progress  one  degree  upwards,  diminished  intervals  downwards. 

The  chromatic  alteration  of  an  interval  «f  the  chord  of  the  seventh  has 


96  MANUAL    OF   HARMONY. 

been,  in  part,  already  mentioned,  where  to  the  chromatically  altered  triad; 
the  seventh  was  also  added  (page  92).  This  occurred  with  the  augmented 
triad. 

Among  the  remaining  secondary  chords  of  the  seventh,  the  chromatic 
alteration  of  one  receives  an  especial  importance.  This  is  the  chord 
of  the  seventh  of  the  second  degree  in  minor,  which,  in  the  following  form, 
produces  chord-formations  much  used. 

The  chromatic  raising  of  its  third 

a:    iio.^ 


7 
gives  the  following  inversions : 


a  4:  ^ 

5.3  2 


Of  these  inversions,  the  second  is  the  most  important  and  is  much  used, 
the  rest  are  unusual. 

The  chord  resulting  from  the  second  inversion  is  known  under  the 
name  of 

THE  AUGMENTED  CHORD  OF  THE  SIXTH,  FOURTH  AND  THIRD. 

Its  progression  is  based  upon  that  of  the  fundamental  chord,  that  is,  as 
the  chord  of  the  seventh  of  the  second  degree  leads  most  immediately  to 
the  dominant,  so  also  will  this. 


185.  3F— ^« — ^ 


IlO, 


If  the  fundamental  of  this  chord  is  omitted,  the  augmented  chord  of  the 
sixth,  already  found,  arises,  the  progression  of  which  to  the  dominant  is 
hereby  explained,  (see  page  94) ; 


With  omiHHion  of 
the  Fundamental : 


1S6. 


^mMmM 


or,  for  comparison  with  No.  179,  in  G  minor : 

Cliro.raiHiug    AuQ.  chord  of  tl'f  ftixth^  Aug.  chord  of 

Fundamental  chord :      of  the  third :        fourth  and  third:  the  sixth  : 


MANUAL    OF    HAR3I0NY. 


9T 


Remark. — It  may  be  mentioned  here,  that  the  formation  of  the  augmented  chortl 
of  the  sixth,  fourth  and  third  can  be  already  reached  through  the  harsh  diminished  triaa 
{hart  verminderter  Dreiklang)  mentioned  page  95,  to  which  a  seventh  is  added;  that 
the  resolution,  however,  must  become  a  different  one,  since  that  was  considered  to  be  on 
the  seventh  degree,  while  this  is  found  upon  the  second. 

Instead  of  the  fundamental  of  this  chord,  the  ninth  of  the  fundamental 
chord  can  be  added,  whereby  the 

AUGMENTED  CHORD  OF  THE  SIXTH  AND  FIFTH 
arises. 

Its  origin  is  as  follows  : 


icWiout  Fundamen tal :    InverHon* : 
Fundamental       with  ninth :       with  elevation         a.    0        b.    0 
chord:  of  the  third:  5  3 


1§§. 


Of  these  chords,  the  one  resulting  from  the  first  inversion  a^  the  aug' 
mented  chord  of  the  sixth  and  fifth^  is  best  adapted  for  use,  the  others 
are  rare. 

Its  natural  progression  is  likewise  to  the  dominant,  but  always  produces 
varalhl  fifths : 


189. 


These  progressing  fifths,  which  do  not  belong  to  the  most  unpleasant  ones, 
are  avoided  either  through  an  earlier  resolution  of  the  fifth  (the  original, 
above-mentioned  ninth  as  suspension),  as  in  the  following  Example  («),  or 
through  a  skip  of  the  same  into  the  third,  whereby  the  augmented  chord  of 
the  sixth  results  (&)^  or  most  frequently,  by  the  third  and  fifth  remaining 
stationary  while  the  sixth  and  the  Bass  tone  progress,  whereby  the  chord 
of  the  sixth  and  fourth  is  inserted  before  the  resolution  (c),  which  chord 
can  be  here  regarded  as  a  prolongation  of  the  suspension. 

a.  b. 


190. 


mm 


not 


.—     '^' 


better . 


=iirii[i^life 


S=F 


Remarb:. — ^The  addition  of  the  ninth  does  not  justify  explaining  this  harmony  as  a 
chord  of  the  ninth ;  the  ninth  has  here,  as  everywhere,  the  same  character  as  suspen- 
aion,  as  appears  very  plainly  from  the  progression  a/  just  so  the  p'-ogression  at  b  and 


98 


MANUAL    OF   HARMONY. 


C  answers  completely  to  the  treatment  of  the  suspensions,  as  it  also  (as  fifth  in  the  aboT« 
chord)  requires  a  preparation. 

It  would  follow  from  this,  that  this  harmony  should  be  taken  into  consideration  first 
in  connection  with  the  suspensions,  it  was  however  necessary  to  mention  it  here,  be- 
cause the  question  of  the  origin  was  under  discussion,  and  it  was  not  the  intention,  by 
the  above  expressed  view,  to  oppose  a  generally  received  appellation. 

Exercises, 
6      6^    «      2 


fmf^ 


4.         3 


3  - 


mm: 


At  the  close  of  this  chapter  we  survey  once  more  the  broad  field  which 
was  opened  in  it  for  harmonic  formations.  We  have  found  much  which  is 
generally  known  and  adapted  for  use.  Much  appeared  to  us  unadapted 
for  use  and  worthless.  Nothing  however  showed  itself  in  its  original  condi- 
tion, everything  had  received  an  addition,  experienced  an  alteration,  in  a 
certain  sense,  adornment.  This  forsaking  of  the  original  gives  us  occasion 
to  refer  once  more  to  that  which  was  remarked  on  page  93. 

A  long  time  indeed  elapsed,  before  these  harmonic  transformations 
were  discovered,  and  a  still  longer,  before  they  became  common  property ; 
much,  which  until  now  is  unadapted  for  use,  may  with  time  be  developed, 
but,  in  order  that  the  healthy  inner  germ  may  not  be  lost,  we  cannot  ad- 
vise the  direction  of  the  whole  effort,  out  of  desire  for  originality,  to  the 
discovery  of  new  harmonic  forms,  or  the  immoderate  use  of  them  and  devia- 
tion from  the  primitive. 

Since  all  these  transformations  serve  more  for  adornment,  and  It  might 
be  said,  for  the  more  elegant  carrying  out  of  the  simple  fundamental  idea, 
we  may  venture  to  use  them  only  with  discrimination  if  wc  do  not  wish  to 
overload  the  work  of  art,  and  thereby  ourselves  be  reckoned  as  without 
taste. 


MANUAL    OF   HARMONY. 


99 


At  the  close  of  the  exhibition  of  all  essential  harmonies  and  their  most 
immediate  use,  may  still  follow  a  brief  view  of  them,  their  varieties  and 
derivatives. 


View  of  all  Chords  belonging  to  a  Major  or  Minor  Key, 

I.    FUNDAMENTAL    HARMONIES. 
a,    Tlie  Triad.  b.    The  chord  of  the  uventh. 


i 


A«     The  varieties  of  the  Triad  : 
Major,  Minor,  Diminished,  Augmented. 


Major  Triads, 

Of  the  Major  Scale  :  Of  the  Minor  Scale  : 


^5 O^ 


C:    r        IV        V  a:    V       VI 

Minor  Triads. 

Of  the  Major  Scale :  Of  the  Minor  Scale  : 


C:    II        m        VI  a:    1         IV 

Diminished  Triads. 

Of  the  Major  Scale :  Of  the  Minor  Scale  : 


C:     viio  a:    11°      vno 

Augmented  Triad  of  the  Minor  Scale. 


A :    IIP 
N.  B. — The  remaining  augmented  triads  see  mider  II. :  Altered  Chordi, 


Inversions  (Versetzungen)  of  the  Triads : 

a,    Tlie  chord  of  the  sixth. 
6 


6.    The  chord  of  the  sixth  and  fourth. 
6 


^ 


4 


o «-- 


100 


MANUAL    OF   HARMONY, 


B.     The  Varieties  of  the  Chord  of  the  Seventh. 

a.     Tlie  dominant  chord  of  the  seventh  or  primary  chord  of  the  seventh 

b.    Secondary  chords  of  the  seventh. 

a»     Dominant  chord  of  the  seventh  (major  triad  with  minor  seyentb). 

Formed  alike  in  Major  and  Minor  : 
7  7  7 


I 


C:     T, 


c:     Yxf    a:  V» 


b.     Secondary  chords  of  the  seventh 
1.  Major  triad  with  major  seventh 


In  Major. 


C: 


IV' 


2.  Minor  triad  with  minor  seventh 

In  Major. 


C:  11^ 


In  Minor. 


:    Ylj 


In  Miner, 


=^= 


3.  Diminished  triad  with  minor  seventh 

In  Major  : 


Jn  Minor  : 


C:    vu«>. 


I 


a:    xi^f 


4.  Diminished  triad  with  diminished  seventh  (chord  of  the  diminished 
seventh) 

In  Minor : 


a:  yiV>, 


$.  Augmented  triad  with  major  seventh 

In  Minor: 


%=\ 


MANUAL    OF   HARMONY, 


101 


Inversions  (Versetzungen)  of  the  Chords  of  the  Seventh, 

a.    The  chord  of  b.    The  chord  of  the  c  Th^  chord  of 

the  %ixth  and  fifth :    sixth,  fourth  and  third :         the  second  : 


m 


^ 


«s«: 


--^-- 


3^ 


II.    ALTERED  (cheomaticallt  changed)  CHORDS. 
a.     The  augmented  triads  formed  from  the  major  triad  : 

In  Major  : 

C:  T  IV  V 

ll«     The  augmented  chord  of  the  sixth,  formed 
1.  From   the   minor  triad   with  raised  fundamental  (so-called  double 
diminished  triad) : 


I 


rfc: 


2.  From  the  chord  of  the  seventh  of  the  second  degree  in  minor.     (See 
the  following  chords) : 

C»     The  augmented  chord  of  the  sixth,  fourth  and  third; 

d.     The  augmented  chord  of  the  sixth  and  fifth, — both  formed  from 
the  chord  of  the  seventh  of  the  second  degree  in  minor : 


With  the  ninth  from 
liaising  of  Second  Without  Fundamental,        the  Fundumental 

ilte  third  :  Inversion  :       aug.  chord  of  the  sixth :   and  without  the  latter. 


fe — J §g 


o:   no» 


^ 


102 


MANUAL    OF    HARMONY. 


CHAPTER    XI. 

On  Jlodiilation  of  a  JPassage  of  Music  (eines  Tonsatzesj. 

The  term  modulation  has  a  various  signification.  ,  Formerly  was  under* 
?tood  thereby  the  way  and  manner  in  which  the  succession  of  harmonies 
is  arranged  to  a  vocal  part.  In  the  later  sense  is  understood  the  digres-f 
sionfrom  one  key  into  another.  The  name,  digressive  modulation^  which 
is  sometimes  found,  would  be  no  pleonasm  according  to  the  original  signi- 
fication of  the  word. 

According  to  the  import  of  the  term,  it  will  next  be  important,  to  learn 
rightly  to  recognize  and  determine  each  occurring  modulation  (digression 
into  a  foreign  key) ;  farther  on,  in  Chapter  XYI.,  the  means  for  modula- 
tion will  be  discussed)  whereby  the  capability  of  recognizing  the  latter  is 
more  fully  supplied.  ,    :        ,.-  :    ' 

A  modulation  arises^  if  a  harmony  foreign  to  the  previous  hey  ap- 
•pears. 

The  previous  key  is  then  wholly  forsaken,  and  the  harmonies  must  be 
reckoned  to  the  new  key,  so  long  as  no  harmony,  again  foreign  to  it,  appears, 
which  effects  a  new  modulation. 

Thus  in  the  following  Example  :  , 


193. 


is  a  modulation  to  D  minor  in  the  third  measure,  because  Cjj-E-G-Bjz, 
belongs  no  longer  to  C  major,  but  undeniably  to  D  minor,  whereas  in  the 
fourth  measure  it  is  doubtful  whether  the  C  triad,  which  is  foreign  to  the 
previous  key  (D  minor),  is  to  be  reckoned  to  C  major,  or  to  the  Gr  major  fol- 
lowing, while  the  modulation  to  A  minor  in  the  fifth  measure  is  unmis- 
takable. 

The  dominant  chord  of  the  seventh^  as  also  the  chord  of  the  diminished' 
seventh^  are,  as  the  chief  means  of  modulation,  never  to  be  mistaken ;  all 
the  remaining  chords  are  amhiguous^  that  is,  they  can  belong  to  several 
keys. 


MANUAL    OF   HARMONY, 


103 


Thus  the  Gr  major  triad  belongs  not  exclusively  to  G  major,  but  is  also 
sub-dominant  to  D  major  and  sixth  degree  to  B  minor. 

This  ambiguity  often  allows  the  modulation  to  bo  recognized  first 
from  the  succeeding  chords,  as  in  fact,  the  decided  motlulation  itself  can 
be  formed  first  through  the  dominant  harmony  of  the  seventh  with  its 
derivatives. 

The  musical  ear  itself  proceeds  very  simply  in  the  apprehension  of  a 
modulation :  it  always  apprehends  the  foreign  haru^vW  as  belonging  to 
that  key,  which  is  nearest  related  to  the  ruling  one. 

Thus,  for  example,  in 


193. 


the  major  triad  of  D  in  itself  considered,  would  belong  to  tl^o  key  of  D 
major ;  in  connection,  however,  with  C  major,  it  will  be  most  imxir^d lately 
recognized  as  dominant  to  G  major,  and  the  following  chords  first  can  de- 
termine which  key  becomes  the  ruling  one. 

There  follow  here  some  more  exercises  for  practice  in  searching  out  tV  > 
modulations;  for  the  farther  discussion  of  this  subject  see  Chapter  XY/ 


194. 


Exercises, 


G 
6Q  5 


C:    I      G:  V,.  1     C: 


IV  Vi 


Tb 6_       5  


izid: 


I    d:  vii°» 


I    C:  I 


liny    V 


wm 


5  2  6       6 


EEIEE^ 


3. 

3 

.  fs  ■  ■ 

6    7b 

b 

6 

6fe 

2 

f    6 

7  3 

6 

9-ir 

=::zz^= 

\-f4- 

(&- 

Et=: 

tili 

1 

-^—i 

=M 

6  7 

4« 


4. 


7b   - 


:i^iPL: 


lE^^^l^i^g^ 


6-7 

4-$ 


^6      ^  2        6 4-$        5. 5  6  jar 


104 


MANUAL    OF   HARMONY. 


t       2 


iy^^3^.li=Jife%^E^li^llPii 


'7_ 


6 
4  7 


I 


6.         3    6  ff 


-=i^33^ 


4  JB^         68 

313  5t5       4    3     6    8  7 


ZICL 


-O +->B 


4 
3b 


4b  4 
3    3 


6b    6 
4      5 


6    6 

5    6  C 

± 


ii^=i=^i^i^^=gEi3^fS^f§Ei 


9Jp=j=l 


6b 


6 

4      7 


3  2  6 


ii^lil^^li^l^l 


I 

6       3 


6b 

4       6 
2       6 


C ^ 52 « —  I — « — it-j Ja — 1 


^ 6 7 

::^~3=::3: 


#^ 


iSz::®: 


1 


The  modulation  can  be  indicated  in  the  same  manner  as  in  the  first 
exercises,  according  to  which  the  letters  indicate  the  key  and  the 
Roman  numbers,  as  we  know,  the  degrees  upon  which  the  chords  in  ques- 
tion rest. 


/ 


MANUAL    OF   HARMONY. 


105 


PAET   II. 

ACCIDENTAL  CHORD-FORMATIONS.— TONES  FOREIGN  TO  THE 

HARMONY. 


CHAPTER    XII. 


Suspensions. 

The  simultaneous  progression  of  all  voices  to  the  following  chord,  par- 
ticularly if,  as  in  our  previous  examples,  it  takes  place  through  no 
metrical  variety  of  the  movement,  produces  a  certain  measured  character 
and  monotony  of  the  musical  sentences. 

A  new  chaining  together  and  binding  of  the  chords,  and  a  thereby  more 
interesting  change  of  harmonic  connections  arises,  if  the  voices  do  not 
everywhere  progress  simultaneously ;  if  one  or  several  of  them  linger  in 
their  places,  while  others  already  form  the  component  parts  of  the  next 
harmony. 

The  most  important  manner  of  thus  linking  harmonies  together,  and  the 
one  to  be  preferred  is  the 

SUSPENSION". 

This  arises  through  the  delaying  of  a  progression  of  a  voice,  which  is  ex- 
pected at  a  definite  time,  or  even  necessary,  and  in  such  a  manner,  that  the 
voice,  which  has  to  progress  one  degree  downwards j  in  order  to  occupy  its 
position  in  the  following  chord,  lingers  still  upon  the  tone  of  the  Jirst 
chord,  while  the  others  progress  to  the  second,  and  this  voice  does  not  pass 
over  into  the  harmony  until  later. 

In  the  toUowing  connection  of  harmony : 


195. 


^^^^ 


ii^i^i^^fi 


106 


MANUAL    OF   HARMONY, 


the  Soprano  can  linger  upon  the  C  during  the  entrance  of  the  second  chord^ 
and  pass  over  later  to  the  B  in  the  following  manner : 


196. 


Just  so  a  suspension  can  be  formed  from  Example  No.  195,  through  the 
delaying  of  the  Tenor  :  ,  ^ 


197. 


;?^=^=Ie^[| 


jiii 


i^[E 


That  which  is  characteristic  of  the  suspensions  is,  that  they  form  a  dis- 
sonance against  the  harmony  with  which  they  appear,  and  that  they  thereby 
act  as  a  means  for  harmonic  connection,  since  they  render  the  necessary 
relations  of  two  chords  more  intimate  through  the  resolution  expected.  In 
this  respect  they  have  a  similarity  with  the  sevenths,  in  common  with  which, 
as  connecting  intervals,  they  require  preparation  as  well  as  resolution. 

The  dissonant  character  of  the  suspension  is,  to  be  sure,  not  always  con- 
tained in  the  interval  of  it  which  disagrees  harmonically  with  any  particular 
voice  ;  cases  can  occur,  where  the  suspension  disagrees  as  interval  with  no 
one  of  the  other  voices,  but  where  the  character  of  the  suspension  appears 
only  through  situation,  position  [in  the  chord]  and  progression ;  as  in  Ex- 
ample No.  197,  where  the  tone  of  suspension  forms  a  chord  of  the  sixth, 
and  where  only  the  unusual  appearance,  as  well  as  the  entire  situation  of 
the  triad  of  the  third  degree,  combined  with  the  progression  of  the  Tenor, 
produces  the  character  of  the  suspension. 

The  above  examples  give  the  rules  necessary  in  the  formation  of  the 
suspensions : 

A  suspension  can  he  formed  with  a  descending  progression  of  a  voice 
hy  degrees,  under  the  following  conditions  ;  it  must 

1.  Be  prepared,  and     .  i » 

2.  Resolve  itself. 

There  will,  therefore,  be  three  things  to  observe  in  connection  witli  t!ifc 
suspension  :  its  preparation,  the  suspension  itself  and  its  position,  and 
its  resolution  (progression). 


MANUAL    OF    HARMONlc, 

a.     The  Preparation. 

The  preparation  of  a  suspension  can  take  place  througli  either  compo- 
nent part  of  a  triad.  The  sevenths  also  are  used  for  preparation, 
although  more  rarely  ;  most  often  the  dominant  seventh. 


fc 


Preparation 
through  the  octave  of  the  Fundamental: 


Through  the  third: 


19S. 


Through  the  ffth 


m^^^^m^m^m 


9  8 


6 
-6^ 


7      - 
4      3J 


C:  I    G:  V 


C:  I 


I    e:  viiO- 


Through  the  dominant  seventh . 
I 


i 


=§-r-^=^ 


4    3 


9    8 

$ 


9i: 


C:    V^ 


-siz: 


a:V 


/^he  preparation  takes  place  upon  the  arsis,  the  suspension  itself 
enters  at  the  thesis.  Besides  this,  the  rule  mentioned  before  (page  71)  ap- 
plies, viz.,  that  the  preparation  may  be  of  a  duration  equal  with  or  longer 
than  the  suspension,  but  not  shorter.  ' 

hm     The  Suspension. 

The  entrance  of  the  suspension  at  the  thesis  has  just  been  mentlo'aci'  ; 
its  position  in  other  respects  should  be  still  more  particularly  explalncf*.. 

The  suspension  can  appear  in  any  voice,  before  an^  interval  of  tM 
triad, — before  the  seventh,  only  in  rare  cases. 


108 


MANUAL    OF   HARMONY, 


Suspensiont  before  the  Octave  of  the  Fundamental: 


199, 


5      — 
4      3 


9:=« 


6         — 
4        3 

— gzz: 


•^9-       ^X    cl 


C;    IV  I  I  V 

Before  the  Jt/th  rarely,  only  in  certain  positions: 


IV 


I 


^p^^ 


r 


gi=EE|E^ 


6       6 


r- 
I    ^ 

2        — 

.bfij*! 


if^i^ 


6       5 

5" 


^4 


P^liiM 


^siE 


C:     I 


F:I 


C:  I 


Concerning  the  suspensions  in  case  of  the  fifth,  reference  may  be  made  to 
that  which  was  remarked  in  connection  with  Example  No.  197.  Thus  the 
first  and  third  examples  will  be  entirely  in  the  character  of  the  suspension, 
while  the  fourth  is  not  to  be  called  a  suspension  at  all.  If  a  seventh  is 
added  to  the  chord,  as  in  the  second  example,  the  dissonant  character  of 
the  suspension  immediately  shows  itself. 
/^  That  the  seventh  can  but  seldom  have  a  suspension,  appears  -from  the 
fact,  that  it  [the  suspension]  would  necessarily  be  formed  in  most  cases  by 
the  perfect  octave,  which  in  and  for  itself  is  only  an  interval  of  reduplica- 
tion, and  can  never  come  into  a  dissonant  position  (a),  except  as  in  the  fol- 
lowing Example  bf  where  the  octave  is  diminished. 


200. 


MANUAL    OF    HARMONY. 


109 


In  the  first  case  the  seventh  will  always  be  a  parsing  one. 
C.     The  Resolution. 

The  resolution  of  the  suspension  ensues,  as  was  remarked  before,  in  tht 
same  voice,  by  a  step  downwards. 

Remark. — Ways  of  resolution  which  deviate  from  this  will  be  shown  later. 

Here  it  is  further  to  be  observed  that 

The  tone  of  resolution  (the  tone  which  is  delayed  by  a  suspension)  can  he 
contained  in^  no  ^ther  voice  ;  only  the  Bass  or  the  lowest  voice  can  receive 
it  without  disadvantage  to  the  harmony. 


a,     not: 


h.    letter: 


c.    not : 


d.    NB. 


201. 


lEfe^EE^ 


X 


^ 


^ 


In  Example  a  the  Tenor  steps  from  A  to  C,  which  last,  in  the  Soprano^ 
is  suspended  by  D;  in  Example  c  the  Tenor  receives  the  G,  which,  in  the 
Alto,  has  the  suspension  A.  Both  reduplications  are  faulty,  especially  be- 
cause they  concern  the  third  and  ffth  of  the  chord.  In  Example  d  at 
NB.,  the  reduplication  takes  place  with  the  fundamental.  In  this  casa 
the  effect  is  better,  especially  if  the  consistency  of  the  leading  of  the  voices 
necessitates  it  as  in  the  following  movement :  /""^^ 


Fundamental : 


Third. 
I         I 


Fifth: 


I  \         ^  —  '  I       -ft"  -rt^ 


202. 


ZSlT. 


<^^-^_ 


i 


Remark. — It  may  still  be  remarked  here,  that  the  doubling  of  the  fundamental 
always  assumes  the  distance  of  at  least  an  octave,  and  that  the  doubling  in  unison  is 
faulty,  e.  g., 


The  suspension  can  indeed  appear  in  such  proximity,  only  between  Bass  and  Tenor,  or 
with  the  voice  which  lies  next  to  the  lowest. 

The  lowest  voice,  commonly  the  Bass,  has,  however,  as  the  one  which 
determines  the  chord,  the  power  of  counterweight  against  the  dissonance 


110 


MANUAL    OF   HARMONY. 


of  the  suspension ;    reduplications  are  therefore  admissible,  if  they  are 
based  upon  a  good  leading  of  the  voices,  e.  g, 

favZty  : 


203. 


The  faulty  progression  of  the  Soprano  and  Bass  in  the  last  example  be- 
comes clear,  if  the  suspension  as  mere  delay  of  the  progression  of  the 
voice,  is  taken  away,  through  which  means  the  open  octaves  appear  : 


204. 


:_.g= 


=m 


a!=gpE^B 


The  relation  is  the  same  with  the  fifth-successions,  which  are  covered 
through  the  suspension : 


205. 


I^g^i 


PIE^ 


S 


Here,  however,  the  considerations  will  rule,  which  are  to  be  had  in  view 
in  the  case  of  the  covered  fifths  in  general,  since  position,  situation,  pro- 
gression can  permit  such  leading  of  the  voices,  without  the  unpleasantness 
of  the  fifths  appearing. 

We  condense  these  remarks  into  the  following  rule : 

The  suspension  does  not  remove  parallel  octaves  and  fifths  ;  the  follow- 
ing progression  will,  therefore,  be  faulty  : 


206. 


Parallel  fifths  of  this  kind  are  not,  however,  to  be  unconditionally  rejected, 
if  through  the  movement  of  the  other  voices  a  compensation  is  made  for 
the  unpleasant  succession,  so  that  they  do  not  appear  too  plainly.  To  give 
positive  directions  regarding  them  is  impossible ;  to  reject  them  always 
would  confine  us  too  much. 


MAIS'UAL    OF   HARMONY. 


Ill 


The  suspeiisions  in  the  Bass,  wliich  occur  oftenest  before  the  third  of 
the  chord  (or,  which  is  the  same  thing,  before  the  chords  of  the  sixth  and 
of  the  sixth  and  fifth),  allow  of  no  reduplication  in  the  other  voices. 


207. 


:g.-=zir 


The  suspensions  before  the  fundamental  and  the  fifth  rarely  show  them- 
selves practicable. 


20§. 


iiiiiiliillE 


The  indication  of  the  suspensions  in  the  Thorough-Bass  notation  is,  in 
A)art,  contained  in  the  previous  examples. 

If  the  suspension  lies  in  one  of  the  three  upper  voices,  its  interval  from 
the  Bass  is  given  at  the  same  time  with  the  resolution,  ^«  i7->  4  3",  9  g  7^ 
[the  remaining  figures  determine  the  chord   where  it  becomes  necessary, 

g.j  the  chord  of  the  sixth  |  ^   the  chord  of  the  sixth  and  fourth  t  T 


:or 


7  6 
4-. 


If  the  suspension  lies  in  the  lower  voice,  the  chance  intervals  of  the 
remaining  voices  are  like  wis©  /indicated  by  numbers,  e.  g.,  gZj  or  in  case 

of  the  chord  of  the  seventh   W- ;  the  dashes  which  follow  denote  that  the 


voices  retain  their  tones  during  the  resolution  of  the  suspension. 

The  suspension  in  the  Bass  is  also  marked  by  a  diagonal  stroke  above  it, 
and  the  corresponding  chord  set  over  the  tone  of  resolution,  which  ia 
plainer  as  concerns  the  latter,  e.  g. 


r—a 


209. 


In  the   succeeding  examples  the  first  manner  is  chosen,  as  the  most 
common. 


llti 


MANUAL    OF   HARMONY, 


Exercises, 


K  6 

4  3      7  6** 


_<a--c_,.— r 


7  6      6  7 
4  3 


2.     3    C       9  8 


3i«.  g.^,^|giS^^|^|gi|^ig^p^ 


C:    I 


ty     V-r    I 


6  7 

4  « 


5  — 
4  - 
3      — 


"7        ^7 
9  8         7 


5 
4  3« 


^^^^^^^^^^^^^ 


:F.i±iip: 


2-7 


6 
7    6 


6      31]   6     jS* 


6-     7- 
6  4     4  3 


ifil^ll-^l^pgipi^^^iPi 


4. 


9  8^ 


itei 


2      6        6  2        6 


^— F^F-g'— i-j;^- 


6 


I^H^^IfS 


5*- 


7  65 

4-         7      7      6 
98      3—     6  6bi     6 


i^i^i 


6-     6 
4  3      6 


iS^ggl 


7)^ 
4-  6 
6        3-4 


7  6  6 


'^-%-^ 


zioiz: 


^ 


-^^izgrlz^l 


6  6  6- 

987       6  6       44  3« 

■    :1 


7. 


6-  5 

6      4  3      2    6       2S 


§E?^fe£3Ei^i 


-ftt^z^EEE^ 


6$- 
^  3-6 

3!j  €      2    —       4    3- 


6         9  8  7 


^^^m^miMwm^mi 


6 
6     6 


6         6  7  6 

6    6    4        6     3  7.6 


4- 
7  6  -     3  2  6 


6-6 
4  3  4 


i^-?Eii£^s^feg^iE^il^ii 


m^ 


6 
7  6  6        6      t       7 


::-?^-=:: 


:3=il 


^ 


It  will  be  to  the  purpose  in  the  working  out  of  these  and  the  succeed- 
ing exercises,  to  separate  the  voices  and  write  eacli  upon  an  especial  staff. 
This  notation,  in  the  manner  of  a  score,  affords  a  Letter  vierw  of  the  course 


MANUAL    OF    HARMONY.  113 

of  CE^ particular  voice,  and  is  m  general  a  useful  preparatory  exercise  in 
score  rJiding. 

Here,  however,  it  becomes  necessary  to  write  the  voices,  which,  in  tba 
pure  harmonic  structure,  must  always  be  conceived  of  as  voices  to  be  sung, 
ia  the  clefs  which  have  always  been  allotted  to  them,  the  knowledge  oi 
which  is  indispensable  to  every  musician.  The  knowledge  of  tlicse  clefd 
can  be  very  soon  attained  by  attentive  practice,  and  through  comparison 
with  those  already  known. 

Remark. — The  Icnowledge  of  the  Alto  and  Tenor  clefs  is  requisite  for  the  understand 
ing  and  reading  of  scores,  since  many  voices  and  instruments  are  exclusively  or  partially 
written  in  these  clefs,  and  the  Soprano  clef  itself,  which  occurs  more  rarely,  affords 
with  various  instruments,  which  are  tuned  in  a  particular  way,  an  especial  facility  in 
reading. 

The  clef  which  is  used  for  the  upper  three  voices.  Soprano,  Alto,  and 
Tenor,  is  called  the  G-clef. 

For  the  lowest  vocal  part,  the  Bass,  the  F-clef  or  Bass  clef  used  before 
is  still  applied. 

The  situation  of  the  C-clef  always  indicates  the  place  of  the  once 
marked  [middle]  C,  and  in  such  a  manner,  that  for  the  Soprano  this  C  ia 
found  upon  the  loivest^  for  the  Alto  upon  the  third^  and  for  the  Tenor  upon 
ilic  fourth  line  J  e.  g. 

Soprano-clefs.  AUo-cUfx.  Tenor-clefn. 

fF=»'— l>5F^-js- ■ 

The  most  common  compass  of  the  voices  exhibits  itself  in  these  clef* 
thus : 


-f-^-^-^Tlllll  lill 


r i  I  I  I  I  I  I  I ! lA 

Soprano-clef.       TT"— i~;~  j~i^~f  ~f~r~i 1 ' 


M?^=^-r^^, 


AUo-clef 


I 
I 
0-ft- 


:ir3=:i='=tipiit-E=Ez£: 


I     I     \_\_\     I     !    I 


_    ^^^^^ 


^=^=f3=t=t=i=t=:^==^«:: 


114 


MANUAL    OF   HARMONY. 


Remark. — The  origin  of  these  various  clefs  from  the  most  simple  foundation,  from  the 
80-called  Tablature  (commonly  a  system  of  ten  lines,  upon  -which  all  the  voices  were 
written,  with  especial  designation  of  the  lines  upon  which  the  principal  tones,  F,  C,  G, 
came  to  stand)  is  interesting,  its  farther  explanation  would  here,  however,  lead  us 
too  far. 

The  easiest  method  of  impressing  these  clefs  upon  the  memory,  is 
probably,  to  observe  accurately  the  position  of  the  0- triad  in  the  various 
voices,  whereby  the  tones  which  lie  between  and  on  each  side  are  easily 
found  out. 

Thus  the  position  of  the  complete  C- triad,  with  doubling  of  the  funda- 
mental, will  be : 

Jn  Vie,  Soprano : 


ff5=' 


In  the  Alto . 


I^E? 


C 


:So-- 


Jn  the  Tenor,  best  in  the  position       5]^. — *— c • 

of  the  chord  of  the  sixth  and  fourth  :     "^    — m —  g 


The  carrying  out  of  the  first  exercise  of  No.  210  in  these  clefs  follows 
here : 
211. 


80PBAN0. 1 


Al.TO. 


iBKOR. 


Hmk. 


¥ 


^: 


53; 


i^ 


m^=^ 


t^B 


-G- 


i^[f 


ii^; 


lis: 


7 
© - 


7      6 
5      — 


1 


^1 


F 
IV 


^7 
II  •v 


The  working  out  of  these  examples  requires,  with  all  observance  of  tho 
rules  thus  far  given,  a  skillful  and  a  freer  leading  of  the  voices  in  relation 
to  their  position,  since  the  necessity  of  a  better  position  of  the  suspension 
often  renders  necessary  even  an  alteration  of  the  position  of  the  voices, 
which  we  have  hitherto  always  endeavored  to  make  as  uniform  as  possible. 

In  this  manner  the  open  position  of  the  voices  will  come,  of  itself,  and 
again  be  necessarily  exchanged  for  the  close  position  where  necessity  and 
conformity  with  the  end  in  view  require  it. 


MANUAL    OF    HARMONY. 


115 


In  tliia  exchange  of  the  position  of  the  voices,  the  following  rules  must 
be  observed : 

The  voices  can  never ^  simultaneously,  move-hy^degrees  or  skip  out  of  their 
nectsscm/  position  from  one  chord  to  another  (foreign  one),  except  in  indi- 
vidual cases  in  the  transposition  of  one  and  the  same  chord  into  other 
positions. . 

Ani/  voice  ca7i  forsake  its  position,  if  one  or  more  remain  stationary  iipou 
one  ton\ 

The  following  carrying  out  of  Exercise  8  of  No.  210,  will  make  this 
plainer  . 


¥ 


213. 

150PRAN» 

Altu. 
Tbnoe. 

Bas'j. 


5    NB 


;iE=T^§ 


© — ^T—- (2 s>- 


o      — 
G :     I       — 


0      _    7      aO^        d       r*-     Bb      El,     Bb      C7    F        7 
IV    —    7     iiO-rBkiii     yI     1       IV     ir:v4    I  Bk  V 


-(2-« 


1    NB.  8 


7 
10 


11 


7    1  Jsp:  V  Y 
12 


rEgEEE^EEgEggE=|JEtJEEJEEg=r: 


-<2— •" : 


i 


m^^^^^m 


%m. 


r.y     Bb     C  00 

BbrV^      1        11     o:    I    IV 


The  following  may  serve  as  explanation  of  this  treatment. 

The  close  position  in  which  this  example  begins,  is  forsaken  in  the  fifth 
measure,  in  which  the  open  begins,  and  remains  until  in  the  eleventh 
measure  the  close  position  again  appears. 


116 


MANUAL    OF    HARMONY. 


This  was  effected  through  a  freer  leading  of  the  Soprano  and  Tenor. 
The  first  makes  a  skip,  in  the  fifth  measure,  out  of  its  position  into  the 
seventh^  El^  (at  NB.),  a  skip  which  can  take  place  if  the  fundamental  is 
already  present  and  remains  stationary  (as  here  the  F  in  the  Bass) ;  in 
like  manner  it  forsakes  the  position  in  the  seventh  measure,  by  a  skip  into 
the  fifth,  G,  the  chord  remaining  stationary,  whereby  the  suspension  cornea 
into  a  better  position.  At  last  the  close  position  is  attained  again  through 
the  better  and  free  leading  of  the  Tenor  in  the  tenth  measure. 

Suspensions  from  JBelotv  Upward, 

Suspensions  from  below  are  only  in  a  few  isolated  cases  to  be  regarded 
as  such  ;  most  progressions  of  this  kind  arise  out  of  the  suspensions  from 
above,  before  treated  of,  through  contraction  (abbreviation)  of  the  same 
with  a  farther  succession  in  a  upward  direction,  e.  g,  , 


313. 


i 


-<g- 


from : 


/ 

/       The  suspension  from  below  can  take  place  in  connection  with  the  pro- 
gression of  the  leading  tone  : 


Ei^=3^3Ei^=E^=I=?:-=l 


m^MMi^mm^ 


Y  also  with  several  intervals,  which  progress  a  half^step  upwards,  especially 
with  those  altered  chords,  which  receive  augmented  intervals  through 
elevation,  e.  g. 


215. 


—  ^ 


Observe  here,  that  as  before,  the  tone  of  resolution  (harmonic  tone) 
must  be  in  no  other  voice  with  the  exception  of  the  Bass.  \/ 

Remark. — The  last  of  the  above  examples  brings  us  the  same  tone-combination 
which  presented  itself  before  (page  64)  as  chord  of  the  seventh  of  the  first  degree  in 
minor,  and  which  was  explained  as  unfit  for  use  as  fundamental  harmony.  (See  page 
74).  That,  in  the  above  application,  it  is  to  be  considered  as  suspension  of  the  leading 
tone,  requires  no  farther  explanation- 


MANUAL    OF    HARMONY. 


117 


Of  other  suspensions,  especially  those  which  progress  a  whole  step  upwards: 

«u  b,  c.  \         d. 


some  show,  of  themselves,  the  unnaturalness  of  their  progression ;  and 
some  the  theory  must  pronounce  not  genuine,  and  unfit  for  use  for  the  pure 
harmonic  structure,  however  often  they  may  find  place  in  the  practice. 
If  these  false  suspensions  should  be  carried  out  after  the  manner  pre- 
viously shown  (No.  213),  faulty  progressions  would  show  themselves,  upon 
which  they  are  based : 


817 


iiii: 


idii.^ 


g-\T»*^ 


Suspensions  in  move  than  one  Voice, 

Suspensions  can  occur  in  more  than  one  voice  at  the  same  time 


Su-fpeyuions 
in  two  voices: 


21§. 


In   three  voices 


m^m 


T7 


The  chord  of  the  sixth  and  fourth  frequently  shows  itself  as  double 
^pension,  e.  g. 


di9. 


I  •*"! 


Freer  Movement  of  the  Voices  in  the  Hesolution  of  the  Stis- 

Xyensions, 

Preparation,  entrance,  and  resolution  of  the  suspension  took  place  in  the 
previous  examples  by  means  of  two  chords,  since  the  voices  which  did  not 
take  part  in  it  remained  stationary  during  its  resolution.  The  same  can 
also  take  place  with  ihree  chords,  whereby  the  interchange  of  chords  and 
the  leading  of  the  voices  becomes  still  richer  and  more  manifold. 

This  takes  place,  if,  during  the  resolution  of  the  suspension,  several  of 
the  remaining  voices,  or  one,  usually  the  Bass,  progress  at  the  same  time, 
and  \  7  this  means  form  a  new  harmony. 


118 


MANUAL    OF   HATtMONY. 


For  example,  by  progression  of  the  Bass : 


330. 


1^4^^^-lEr#£l^i1ii[E 


1  — 


IV     II- 


I  a:  viio- 


By  progression  of  more  than  one  voice : 


331. 


^^=1=;;: 


isimiHE^piiilia^lil 


\       1  6         9       6 


^- 


^^^^^^^^^^^  • 


C:    I 


II      V. 


IV      Til*'        VI 


a:  Vh 


In  all  these  examples  the  resolution  of  the  suspension  ensuci  regularly 
during  the  progression  of  the  remaining  voices  to  a  new  harmony,  of  which 
the  resolution-tone  is,  itself,  a  component  part. 

Remark. — ^It  may  here  be  remarked,  in  explanation  of  tlie  view  conceruLag  chords  of 
the  ninth  expressed  in  Chapter  IX,  that  many  places  in  which  the  ninth  occurs,  and 
which  are  recognized  by  many  as  chords  of  the  ninth,  can  be  explained  iu  the  above 
manner;  as  in  Example  221  h,  where  the  cadencing  Bass  progression  F-B  could 
be  easily  explained  as  the  progression  of  a  secondary  chord  of  the  seventh  and  ninth,  if 
the  above  explanation  of  a  suspension  of  a  ninth  with  the  use  of  three  chords  were  not 
much  more  simple  and  did  not  lead  to  the  same  result,  and,  as  with  all  subsequent  ex- 
amples,  present  itself  in  the  same  manner : 


Suspension  of  a  ninth 
•with  two  chords : 


•with  three  chords : 


better : 


222. 


illli^iiPiii 


__. — 5- 


Concerning  the  ninth  which  enters  free,  we  will  speak  later  in  council  tion  with  the 
Oigan-point. 

It  may  still  be  added  as  completion  of  what  was  said  in  Chapter  IX,  t?iAt  as  a  reason 
against  independent  chords  of  the  ninth,  the  impossibility  may  apply,  of  bringing  them 
into  such  inversion  with  the  fundamental,  that  the  latter  is  brought  into  Mtimediata 
proximity  with  the  ninth,  as  can  always  take  place  with  the  chords  of  the  seventh,  e.  g. 


I 


MANUAL    OF    HARMONY, 


119 


7 

Q- 


\      .      I 


223. 


3= 


'M^m^m 


In  the  same  manner  four  chords  can  be  applied  witli  the  suspension,  if 
it  stands  before  a  harmonic  tone,  which  is  not  contained  in  the  remaining 
voices,  e.  g. 

WiUiout  su»pen»ion: 
1_       2     3     4  1        2     3     4 


224. 


:-^: 


6 


iiEE=5_^ 


-go-F-^ 


:?cl 


} 
9      5      6 

1      4 


Pi 


9fE| 


-*— -^^ -.--t- 


^'- 


mmm 


lie: 


C: 


IV       II    vito     VI 


Exercises* 


3-  5    6  6 

8  7    9    6       4    4    7       4  „7 


225. 


•'•i^i^^^ll^l^ 


7    7 


_  2.  8^ 


5  6  7 

4    6    7       4-3 


2      5 

11 


7  JB- 


rqiz: 
-o — 


^S: 


9      6 

7      5 

=1=^=1- 


6 
4  7 


i^=i 


ifeE?^ 


5       ^ 
4      2 


6  73      9      6    — 


5 
4      6 


:|-jz=:izzf-f-[^ — r-j- 


5 

4      6 


7  6- 


6    — 


6      6  6. 

6  5      4      7 


6 

S  7 


7 

4  6 
8  S  4 


6       6- 
4         5 


9:5 

^.-^_ 


L-nLg-tizzici 


/ 


^ 


9       6 

-^ — :1: 


MANUAL    OF   HARMONY, 


7  -  5 

7        432        7       367       46 


6 

■±±.V-X:.—4=.-rA 


E:E3EE35 


6 

7  4     7 


1 


6        S 
5       4  7 


IB 


8       6         4        7 


-"-£; 


^: 


tE 


:»=i 


111 


6 
3      2      5 


-      6 


43 


3       6 


5^Si^il=^i^pglEEiiEMl^jfeip^ 


7  0  7- 
4  —  6  5 

I  3  2    6 


7        - 
4        3 


9     6 


5  — 
7       9    6    4  3« 


^Ie=^je=e^e 


^illii^flliei^ll 


Beiiveen  suspension  and  resdntiony  other  tones  can  he  inserted  in  tha 
same  voice. 
These  can  be : 
1.  Tones  which  belong  to  the  ehord^  e,  g»  ■    m 


=-1-?-- J-, 


2.  Tones  foreign  to  the  harmony,  changing  notes,  e.  g. 


227.  3^-s~irs- 


H- 1  ..J_  t 


^^piielliiili^l 


The  explanation  of  these  and  similar  instances  is  completed  through  the 
exhibition  of  the  passing  and  changing  notes  found  farther  on. 

Instances  also  occur,  in  which  the  suspension  receives  no  resolution 
at  all,  e,  g. 


Usually  in  this  manner : 


-4-4-, 


22§. 


-h-4-i 


They  have  arisen  from  the  following  passages,  by  omissioia  : 


MANUAL    OF    HARMONY, 


121 


229. 


Anticipation,    (Voraitmahme.) 

The  anticipation  of  a  tone,  which  is  more  rarely  used  than  the  saspen- 
sion,  is  the  opposite  of  the  latter,  and  consists  in  this,  that  one  or  more 
voices  allow  some  tones  of  the  next  following  chord  to  be  heard  earlier 
than  others,  and  before  the  metrical  division  allows  us  to  expect  them. 

With  notes  of  long  duration,  and  in  a  slow  movement,  this  manner  of 
leading  the  voices  occurs  seldom  or  not  at  all,  since  the  harshness  of  the 
dissonances  which  appear  here  would  amount  to  unintelligibleness;  it  is 
mostly  shorter  parts  of  measures  which  are  anticipated,  e.  g. 


230. 


Anticipation  in  Vie  Bass 


Jn  the  Soprano  : 


In  several  voices : 


mm 


The  similarity  of  this  movement  of  the  voices  in  its  metrical  form,  with 
that  which  general  musical  instruction  comprehends  under  the  name 
syncopated  notes,  is  not  to  be  mistaken ;  the  latter,  however,  are  formed  not 
by  anticipation  of  the  chords,  but  by  after-striking  (Nachschlagen)  of 
them,  or  they  have  merely  rythmical  significance. 

The  movement  of  the  voices  can  here  also  be  freer  under  some  circum- 
stances ;  for  example,  a  harmonic  tone  can  be  anticipated,  other  than  that 
which  is  intended  at  the  entrance  of  the  chord,  as  in  the  known  closing 
formula  : 


231.  :£zi=:^ 


ZJSZl 


-■$.- 


¥ 


s 


1 


As  antithesis  to  anticipation  may  yet  be  adduced  the  after-striking  of 
harmonic  tones,  which  has  a  similarity  with  the  s'iispensions,  in  so  far,  as 
also  here  pi'eparation  and  resolution  take  place,  but  differs  again,  mate- 


121 


MANUAL    OF   HARMONY. 


rially  as  its  character  expresses  itself  more  in  the  metrical  and  rythmical 
movement,  for  which  reason  it  also  always  appears  in  more  extended  suc- 
cessions ;  the  suspensions,  however,  appear  under  entirely  other  conditions, 
singly  or  in  greater  numbers. 

The  following  Eass  would  be  a  succession  of  such  after-struck  tones : 

Allegro. 

232. 


1~S~ 


t-gi- 


i 


. _ V^-^-f G 


^^m^^mmm 


Here  would   also   belong   that   unison   passage   from   the   overture  to 
Leonore  "  (No.  3)  of  Beethoven  : 


233 


^dzzjzrzt^dzdr:: 


-A-A-A^ 


cresc. 

±44  J jr. 


^■^   It  T5»-- '-#  ^  -S^^ 'T^  ■♦   ^^ '♦    •     ^-^ '•  ft^  ^ 


iAi^m^E^ 


•*.  •* 


"fife   £  £ie 


MANUAL    OF   HARMONY, 


123 


CHAPTER    XIII. 

The  Organ  Point,     Stationary  Voices, 

An  especial  manifold  character  of  the  harmonies,  and  a  mingling  of  them, 
arises  by  means  of  one  or  even  more  than  one  of  the  voices  remaining 
stationary  upon  one  tone,  and  by  means  of  the  chords  thereby  accidentally 
formed. 

"We  frequently  meet  (particularly  in  the  Bass)  as  well  at  the  beginning 
of  a  composition,  as  in  the  middle  and  at  the  conclusion,  at  the  point 
where  the  cadence  should  begin,  with  a  long  sustained  tone,  during  the 
continuance  of  which  the  remaining  voices,  apparently  without  reference  to 
it,  continue  their  harmonic  movement. 

If  this  tone  lies  in  the  Bass,  it  is  called 

ORGAN-POINT    [Pedal  Point]  ; 

if  such  prolonged  tones  occur  in  the  other  voices,  the  lattei  arc  called 

STATIONARY  VOICES  oa  STATIONARY  TONES. 

Remark. — Many  give  these  last  also  the  name  Organ-Point,  but  incon-ectly. 

The  tones,  which  are  adapted  for  remaining  stationary  are  the  tonic  and 
dominant ;  they  also  occur  together. 

Remark. — Attempts  witli  the  third  of  the  triad,  which  in  later  times  have  been 
instituted  by  many  composers,  betray  too  plainly  to  the  ear  the  unnatural  tind  far  sought. 

The  harmonic  connection,  as  well  as  the  progression  of  the  remaining 
voices  takes  place,  always,  during  the  organ-point,  according  to  the  known 
rules,  so  that  the  next  lower  voice  assumes  the  conduct  of  the  harmony, 
and  in  general  without  regard  to  the  stationary  tone. 

Before  we  enter  more  particularly  into  the  manner  of  treating  the  organ- 
point,  some  examples  may  follow. 


231. 


Organpoiitt  upon  the  tonic: 
I 


ij , 


124 


MANUAL    OF   HARMONY, 


6.      Upon  the  dominant: 


'  ^     I  i  r  1 


d. 


Upon  both  at  the  same  time: 


n 1 Z     J        j^^^        ¥:        ^,tj        I       Ij 


§»iEE 


:=iz|-iaziiziiziiz:{:_ciz^       zzqzii 


-<5 


In  these  examples,  those  chords  to  which  the  Bass  tone  does  not  har- 
monically belong,  are  marked  by  a  cross. 

The  following  remarks  may  serve  for  the  treatment  of  the  organ-point : 

1.  The  entrance  of  the  organ-point  takes  place  at  a  rythmically  definite 
time  ; 

2.  By  means  of  a  chord  to  which  the  Bass  tone  harmonically  belongs  ; 

3.  The  last  chord  of  the  organ-point  must  likewise  he  in  harmony 
with  it. 

The  first  takes  place  at  the  beginning  or  close  of  a  period  or  division 
of  one,  and  upon  the  thesis  ;  the  second  and  third  commonly  by  means 
of  the  fundamental  of  a  triad,  as  in  Example  No.  234  a,  Cf  d^  or  at  &, 
through  the  chord  of  the  sixth  and  fourth. 

Care  should  be  taken,  further,  that  the  chords  foreign  to  the  Bass  tone 
do  not  succeed  each  other  too  frequently,  but  are  often  interchanged  with 
chords  to  which  the  organ-point  harmonically  belongs.  This  is  necessary, 
in  order  to  avoid  digressions  violating  the  character  of  the  organ-point 
which  is  only  to  be  found  in  the  holding  firmly  together  of  various 
chord-combinations. 


MANUAL    OF   HARMONY. 


125 


Thus  the  following  organ-point  would  be  faulty  in  this  regard  : 


1      ^    ^      ^ 
J      J     I       I      ^    "^ 


^  J- 


i^fi^psifp^ip^ 


835. 


The  voice  lying  next  to  the  Bass,  in  a  four-voiced  movement,  the  Tenor, 
becomes,  in  case  of  the  organ-point,  the  fundamental  voice  of  the  harmonic 
leading.  Therefore,  all  necessary  harmonic  progressions  will  be  condi- 
tioned by  this  voice,  even  if  the  organ-point  should  also,  accidentally,  belong 
to  the  harmony.  Thus,  in  Example  No.  234  a,  the  progression  of  the  Bb 
in  the  Alto  (in  the  first  measure)  is  determined  by  the  leading  of  the 
remaining  voices,  and  not  by  the  circumstance  that  it  is  seventh  to  the 
Bass. 

If  the  organ-point  stands  upon  the  dominant,  as  is  often  the  case  at  the 
close,  no  plagal  close  can  be  formed  upon  it,  as  appears  already  from  the 
third  of  the  above  adduced  rules,  e.  g. 


236. 


'F — F— "-h- 


NB. 


i    t    t^    I    I    f  r  r  f-  St     * 


The  plagal  close  can,  however,  ensue  with  the  organ-point  of  the  tonic : 

I 


237. 


i I_J_^_J_JfL_iL_JL,__| 1 I ^ ,| ^ ^ 


The  end  of  the  organ-point  is  indeed  to  be  just  as  carefully  treated  as 
its  entrance.  In  the  examples  brought  forward  above,  this  always  takes 
place  through  a  cadence.  In  this  case  it  presents  no  difficulty,  except  in 
instances  such  as  at  No.  236.  The  organ-point  can,  however,  also  pass  over 
earlier  to  the  harmonic  leading,  and  then  the  third  rule  is  to  be  carefully 
•bserved,  e.  g. 


126 


MANUAL    OF    HARMONY. 


I   V 


I      I 


33§. 


-j — I- 


::i= 


iillll 


I       I 


nr^-T 


&c. 


9iEE; 


^^^ 


Breaking  off  in  the  following  manner  would  not,  however,  be  good 

,      J      I       I  J.   J     I       J ,    J 


•fcc. 


w^^mmmm 


339. 


Stationary  Voices* 

Upper  or  middle  voices  remaining  stationary  upon  one  tone,  in  the  man- 
ner of  the  organ-point  before  described,  are  much  more  rare  than  the 
latter,  and  require  greater  caution  in  their  treatment. 

Sustained  tones  of  this  kind  only  conform  to  the  character  of  these 
voices  if  chords  not  belonging  to  them  appear  very  rarely  in  connection 
with  them,  since  such  voices  do  not  possess  the  power  of  counterweight 
against  foreign  chords,  which  is  peculiar  to  the  Bass  or  the  lower  voice  as 
the  determining  one. 

Thus  the  organ-point  of  Example  No.  234  a^  being  transposed  into  the 
upper  voice,  will  in  the  last  measures,  sound  very  unpleasant : 


IS'lO. 


ft^m 


I       1 


^.-A- 


'III, 
1- — c 1 t:_p ^_c:_[:_p_|-iiip — f— f-p — ti 


while  the  following  tone,  prolonged  as  dominant,  is  better  because  the  last 
chords  of  the  example  belong  to  it : 


941. 


:e 


M-i-'=n^7 


_c- 


[I 


v^^.     ^"^ 


MANUAL    OF    HARMONY. 


127 


As  example  of  effective  use  of  stationary  voices  and  prolonged  tones 
Rnd  for  their  treatment,  a  place  can  be  adduced  in  the  "  Gloria  "  of  Che- 
rubini's  Mass  in  C-major,where  the  violins  hold  AJ?  for  a  length  of  time, 
while  the  choir  and  instruments  taking  part,  carry  out  below  it  their  par 
ticular  melodic  and  harmonic  progressions ;  just  so  the  D  of  the  violins 
in  the  introduction  to  the  overture  "  Meeresstille  und  gliickliche  Fahrt  " 
of  Mendelssohn  Bartholdy.  In  both  cases  but  few  chords  can  be  found, 
to  which  the  prolonged  tone  would  not  be  harmonic. 

Uiider  this  head  may  also  be  reckoned  the  Trio  of  the  Scherzo  of  Beet- 
hoven's Symphony  in  A-major,  which  is  based  throughout  upon  the  A 
which  shows  itself  sometimes  as  stationary  tone  in  the  upper  and  middle 
voices,  sometimes  as  organ-point  in  the  lowest  voice,  and  serves  throughout 
the  whole  piece  as  basis. 

Stationary  tones  in  the  middle  voices  are  to  be  treated  with  the  samo 
care,  as  those  in  the  upper  voice.  In  iustrumental  compositions  they 
always  appear  strengthened  according  to  the  circumstances ;  in  the  four- 
voiced  movement  they  occur  rarely  and  not  in  too  great  length,  e.  g. 


—A- 


]— I- 


:fcEz:^z:_*-^izii=:;i»-fii=:Ei:z:tt 


212.    / 


Remark. — As  completion  of  what  was  said  of  the  chords  of  the  ninth,  the  following 
may  here  still  find  place : 

In  the  foregoing  Example  &,  if  the  stationary  voice  be  included  [in  the  reckoning], 
a  complete  chord  of  the  ninth  is  fomid  in  an  inverted  position  with  regular  resolution. 
It  has  already  been  remarked  in  objection  to  the  chords  of  the  ninth,  that  their  inver- 
sions cannot  be  so  used  that  fundamental  and  ninth  are  brought  into  immediate 
proximity,  as  in  the  case  of  the  sevenths.  That  they  can  occur  together  at  greater  dis- 
tances, as  above,  furnishes  no  ground  for  regarding  them  as  independent  chords,  since 
they  occur  only  in  the  relations  there  found,  viz.,  in  connection  with  a  stationary  tone, 
the  character  of  which  is,  however,  also  to  bear  harmonies  foreign  to  it,  as,  for  example, 
is  the  case  with  the  following  ninth,  which  certainly  forms  no  chord  of  the  ninth. 


243.  ; 


i#l^i^llil!E 


I   I    I 


Ti^E 


E^E 


iiil 


128 


MANUAL    OF   HARMONY. 


If  we  wish  to  mark  by  numbers  tbe  harmonic  progression  above  the 
organ-point,  they  must  always  have  reference  to  the  stationary  tone  in  the 
Bass,  whereby  in  many  cases  the  otherwise  general  marking  of  the  chords 
is  altered. 

Thus  the  organ-point  found  under  No.  234  h,  could  be  marked  thus : 


9 
G    -    7     6 
4    —    5     3lr 


9 

7     6 
4    4 


244. 


S=l^ 


9  9 

7     6     7     7 
5    4  4 


8 
7     6    4    7 
4    2 


m\ 


Such  a  manner  of  marking  is  only  used  for  especial  purposes,  on  ac- 
count of  the  difficulty  of  reading  it  and  also  its  incompleteness,  for  which 
reason,  in  scores  where  a  figuring  is  introduced,  we  often  find  with  the 
organ-point  the  words  tasto  solo,  which  indicates  that,  with  the  otherwise 
customary  organ  accompaniment,  only  the  organ-point  itself  is  to  be  given. 


CHAPTER  XIV. 

Passing  Notes,    Changing  Notes, 

Among  the  tones  foreign  to  the  harmony  are  especially  to  be  reckoned 
the  passing  and  changing  notes. 

The  first  arise  through  the  filling  out,  by  means  of  tones  lying  between, 
of  greater  or  smaller  harmonic  voice-steps,  e.  g. 


245. 


Efe^: 


t: 


The  notes  marked  by  a  cross  x  form  the  pass^  those  marked  with  a  0 
are  harmonic  by-tones,  that  is,  in  so  far  as  with  the  first  note  a  C  or 
A-triad  can  be  conceived,  e.  g. 


MANUAL    OF   HARMONY. 


i — -!-i— ©- 


245. 


i 


ii^^[iiepl^ 


12i» 


The  passing  notes  found  under  a  of  Example  No.  245  are  called  dia- 
fonic,  those  under  b  chromatic  passes. 

The  passing  notes  go  from  one  harmonic  note  over  to  another  har- 
monic note;  they  appear,  therefore,  not  with  the  entrance  of  the  chord,  but 
after  it,  upon  smaller  divisions  of  the  measure,  and  can  be  introduced 
only  in  progression  hy  degrees. 

Changing  notes,  on  the  contrary,  are  those  tones  foreign  to  the  har- 
mony, which  either  appear  in  the  character  of  a  suspension  or  appog- 
giatura  at  the  time  of  the  entrance  of  the  harmony  (thus  in  this  sense  upon 
the  accented  part  of  the  measure),  and  attach  themselves  to  the  harmonic 
note  (No.  247  a),  or,  after  the  manner  of  the  passing  notes  upon  the  unac* 
cented  part,  serve  for  the  melodic  adornment  of  two  like  notes,  .(No. 
247  h). 


The  changing  note  can  therefore  appear  in  skips,  it  must  however  be 
joined  closely  to  the  harmonic  note,  as  the  examples  in  No,  247  show. 

It  is  further  to  be  seen  from  the  above  examples,  that  the  chan^^ing 
notes  can  be  formed  by  the  note  which  lies  immediately  helow  th^  har- 
monic note,  as  well  as  by  the  one  which  lies  immediately  ahove. 

The  changing  note  helow  the  harmonic  note,  especially  if  it  enter  after 
the  manner  of  an  appoggiatura,  upon  the  accented  part  of  the  measure,  has 
the  peculiarity  that  it  inclines  to  form  a  minor  second  to  the  principal 
note,  whereby  chromatic  tones  arise,  as  is  to  be  seen  from  No.  247,  hence 
the  formation  of  movements  like  the  following  would  not  be  admissible : 


130 


MANUAL    OF   HARMONY. 


248. 


I 


This  applies  particularly  to  the  changing  notes  introduced  by  skips. 

It  is  otherwise  if  they  appear  in  a  progressing  series,  whereby  they  tale 
on  the  character  of  the  passing  notes.  Thus  the  following  series  of  chang- 
ing notes  at  a  would  not,  of  necessity,  be  so  formed  as  at  b, 

^      y      jf 


249. 


till 

Those  changing  notes  below,  which  fall  upon  the  unaccented  part,  require 
only  partially  the  minor  second.  Thus,  in  the  Example  No.  250  a^  the 
formation  will  not  necessarily  be  like  h^  while  c  is  not  so  good  as  d^ 


250. 


d. 


^^^ 


-k 


--i-^ 


I 


t  I  I 

Definite  rules  on  this  head  cannot  be  given ;  it  is  also  unnecessary,  in  a 
.■Mich  as  every  musical  ear  will  certainly  find  that  which  is  right. 

Semark. — ^The  third  of  the  triad  bears  the  changing  note  as  whole  step  better  than 
Iki  fifth  and  octave.  Since  with  the  latter  the  changing  note  can  appear  at  the  same 
fiiae  as  seventh,  so  that  the  succession  only  can  determine  in  respect  to  it. 

C]lia:iging  notes  above  the  harmonic  note,  whether  they  enter  free  (by 
skips),  or  in  the  manner  of  No.  250,  can  form  major  or  minor  seconds  to 
the  chord-tone  because  they  are  always  formed  diatonically,  and  govern 
themselves  according  to  the  key  and  modulation. 


251. 


I      I     I 


I    J     I 


i=:-=^ 


i 


I       I       1 

We  often  meet  with  figures,  in  which  changing  notes  above  and  below 
the  chord  note  are  made  use  of  one  after  the  other,  e.  g. 


252. 


f=j r 


MANUAL    OF   HARMONY. 


131 


Upon  this  is  founded  also  the  following  often  occurring  manner  of  em 
bellishment : 


253. 


$^^m 


Passing  and  changing  notes  can  occur  in  all  voices.  If  this  takes  place, 
by  preference,  in  one  voice  alone,  this  one  will  become  prominent  in  com- 
parison with  the  others,  and  receive  a  concerting  character,  while  the 
remaining  voices  serve  for  accompaniment.  If  this  should  not  be  the  case, 
all  the  voices  can  be  made  prominent,  interchangeably,  by  such  by- 
tones,  and  gain  thereby  in  significance.  Wherever  the  position  and 
progression  of  a  voice  adapts  it  for  the  introduction  of  such  by-tones,  it 
will  by  this  means  admit  of  more  significant  melodic  development ;  but 
here  also  the  proper  mean  must  be  found,  since,  otherwise,  over  fullness  and 
a  lack  of  clearness  can  easily  arise. 

The  following  simply  harmonic  movement, 


254. 


■^^111=^^ 


I 


^i:^fE^±Emm^f 


:^ 


~-^- 


^        V 


I        I 


t — r 


iM^E 


miglit,  by  the  use  of  the  above  by-tones,  assume  the  following  form  : 


255. 


132 


MANUAL    OF    HARMONY. 


w zzz: 0 — ^_1  ®__A ^— ±-o a 1.?^ s,__fzl-ssizil:t 


The  passing  and  changing  notes  are  here  marked  by  crosses  x. 

That  through  such  copious  use  of  tones  foreign  to  the  harmony,  the  pas- 
sage can  easily  suffer  from  overloading,  is  to  be  seen  in  the  above  example 
if  it  is  executed  in  a  somewhat  rapid  tempo  ;  a  slow  movement  is  better 
adapted  to  this  manner  of  writing. 

In  the  introduction  of  the  changing  notes,  care  is  to  be  taken,  as  was 
before  remarked  in  connection  with  the  suspensions,  that  no  voice  receives 
the  harmonic  tone  which  in  another  is  introduced  through  a  changing 
note,  e.  g. 


256. 


This  can  only  occur  if  the  distance  of  the  harmonic  tone  from  the  tone 
foreign  to  the  harmony  is  at  least  one  octave,  e.  g. 


257. 


1      I 


i 


^^^m^m 


This  reduplication,  according  to  the  principles  of  reduplication  in  gen- 
eral, will  take  place  better  with  the  fundamental  or  fifth,  than  with  the 
third  of  the  fundamental  chord. 

In  a  rapid  movement,  however,  and  more  extended  carrying  out  of  such 
figures  formed  through  changing  notes,  other  considerations  arise,  as  the 
following  passage  shows ;  this  to  be  sure,  cannot  be  conceived  of  as  a  four- 
voiced  vocal  movement : 


In  the  case  of  the  regular  passing  notes,  like  regard  is  to  be  had  to  their 
approximation  to  harmonic  tones,  and  figures  such  as  No.  259  a,  &,  do 
not  appear  so  pure  as  c,  dj  €• 


259. 


MANUAL     OF    HARMON  7. 
h,  e,  d» 


133 


(2- 

-|-—fi>-#- 


-i2- 


^^f=f-r^:^===-^fSFf-T=f^TT^ 


^^l 


3Iore  rapid  figures  allow  this  approximation  more  readily,  e.  g. 


260. 


~i— I — I — F-# -j L •  •- 


"Sij 


faulty  Progressions  in  Connection  with  Passing  and  Changing 

Notes, 

Since  it  is  the  province  of  the  passing  notes  to  fill  out  the  movement  in 
skips  of  the  harmonic  progression,  we  must  take  care  in  connection  with 
the  change  of  the  harmony,  that  no  false  progressions  arise,  as  in  the  fol- 
lowing examples,  from  covered  fifths  opeji  ones  arise : 


a.      , 


261. 


giSii: 


--^ — j- 


•*W        I 


-rr-r^ 


I  r  I 


Open  octaves  formed  with  passing  tones  cannot  occur,  because  the  first 
of  them  will  be  harmonic  as  much  as  the  second. 


262. 


-J-^ 


^rrrr 


i 


On  the  other  hand,  in  the  following  instances,  the  passing  notes  will  not 
cover  the  open  octaves,  and  consequently  will  be  considered  as  faulty  * 


263. 


Remark. — The  last  tind  of  octaves  would  find  application  in  instrumental  movements, 
•aoder  the  condition  of  intended  strengthening  and  reduplication. 


134 


MANUAL    OF   HARMONY. 


In  like  manner  the  entrance  or  progression  of  the  changing  note  in 
parallel  movement  is  to  be  called  faulty  if  it  takes  place  in  the  following 
manner : 


261. 


letter : 
I 


^^= 


I  J   _j 


— ©=>=^— ©— , -; 


T- 


-f2- 


mm^t 


I  I 


ii; 


:i^^ 


-(2-^=^ 


.-- i^ 


The  last  example  is  better  because    the  octave    progression  appears 
covered. 


Passing  and   Changing  Notes  in  more  than  one  Voice  at  the^ 

same  time,  r  fl 

The  movement  of  the  passing  notes  in  more  than  one  voice  at  the  same 
time  is  best  adapted,  in  parallel  motion,  to  the  successions  of  thirds  and^^^ 
sixths,  e,  g.  fl 


265. 


t=^— 


l=^fIE]^^E^=lh= 


J^fr^^^ 


1 


^ 


The  free  movement  of  the  voices  with  the  use  of  the  passing  notes  can 
also  produce  parallel  seconds,  fourths,  fifths,  and  sevenths,  of  all  kinds, 
which  require  great  caution  in  their  treatment,  and  on  account  of  their 
disagreeable  effect  are  only  to  be  allowed  singly ,  and  in  a  very  favorable 
position. 

Progressions  in  fourths  are  good  if  a  third  voice  is  added  as  third 
below : 


266. 


jgl3r4mliB 


Single  fifth-successions  arising  from  passing  notes  are  occasionally  met 
with  in  good  compositions,  which,  however,  is  no  reason  for  recommendicg 


I 


MANUAL    OF    HARMONY. 


135 


them  as  faultless.  (See  that  "which  is  said  concerning  fifth-successions 
page  27  and  what  follows). 

Just  so  the  harshness  of  the  seventh-successions  can  only  be  alleviated 
through  favorable  position  and  good  leading  of  the  voices  throughout ; 
indeed,  through  tempo,  movement,  etc. 

In  contrary  movement  the  various  intervals  of  the  passing  notes  often 
give  to  the  passage  an  especial,  peculiar  coloring,  and  contribute  much  to 
the  independence  of  the  voices,  but  they  must  not  appear  too  numerously 
and  in  too  many  voices  at  the  same  time. 


I 


•H — iji — ^-G T-* — I— ^F^ — 1^*^— — r  r 

^  -rzi   ^  I  ^^ 


Here  also  it  will  be  found,  that  those  passing  notes,  which,  outside  of  the 
simply  harmonic  structure  lying  at  the  basis,  form  with  others,  as  it 
were,  a  most  intimate,  new  (passing)  harmonic  leading,  are  more  natural 
and  milder  than  those  whose  collocation  cannot  be  harmonically  ac- 
counted for. 

A  judgment  concerning  the  worth  of  such  movements  can,  however,  b€ 
arrived  at  only  by  taking  into  consideration  their  character  and  tempo. 

In  case  of  regular  harmonic  progressions,  several  voices  can  receive  pass- 
ing tones  at  the  same  time,  e.  g. 


30§. 


In  all  such  places  everything  depends  upon  the  question,  whether  at  the 
hange  of  the  harmony  the  voices  are  in  a  position  which  allows  them 
0  form  their  progression  regularly. 

Changing  notes  can  occur  in  various  voices  : 

a.     In  tivo  voices : 


136  MANUAL    OF   HARMO.¥T. 

in  pa  -allel  motion : 

869.  gz!»;p^=E3t=PE:^r|S=?=K^^^L=: 


I 


in  contrary  motion: 


( 


aro. 


9: 


[^ 


b.     In  /Are^  voices : 


271 


1     I     t 


In/( 


our  voices : 


I     I 


^,^ 


Remark. — ^The  most  of  the  above  examples  can  also  have  the  force  of  harmonic  pro 
gressions  with  the  organ-point. 

It  becomes  evident  from  these  examples,  that  also  in  the  parallel  move- 
ment of  two  voices  in  changing  notes,  the  progression  in  thirds  and  sixths 
appears  most  natural,  while  the  parallel  seconds,  fourths,  fifths  and  sevenths 
always  produce  a  very  disagreeable  effect.  Thus  no  one  ^-ould  be  likely  to 
pronounce  changing  notes  of  the  following  sort,  good  : 


good 


273. 


Changing  notes  can  also  be  of  longer  duration,  than  the  harmonic  note 
io  which  they  are  joined,  e.  g. 


274. 


i£ilp!i^4%iij| 


mmm 


I> 


MANUAL    OF   HARMONY.  137 

The  significance,  in  composition,  of  the  subjects  explained  in  Chapters 
XII.,  XIII.  and  XIY.,  is  great  enough  to  subject  them  to  a  careful  inves* 
tigation ;  as  a  thorough  knowledge  of  them  contributes  materially  to  the 
understanding  of  the  inner  harmonic  structure.  We  have  still  to  speak 
concerning  their  relation  to  the  pure  harmonic  structure — the  object  of 
our  immediate  studies. 

Since  on  page  24  the  term  "  pure  harmonic  structure  "  was  only  spoken 
of  in  a  general  way,  it  becomes  necessary  to  consider  the  question  more 
narrowly,  and  to  present  it  something  in  this  manner  : 

What  application  of  these  meayis  for  composition  does  our  immediate 
purpose,  {the  exercises  in  the  pure  harmonic  strudure)^  allow  ? 

It  is  undeniable  that  these  means  are  particularly  adapted  for  develop- 
ing and  adorning  the  voices. 

If,  however,  our  most  immediate  work  is  the  recognition  and  carrying 
out  of  simple  harmonic  formations,  then,  to  be  sure,  everything  which  is 
adapted  to  develop  the  voices  will  be  appropriately  used ;  but  anything 
else,  serving  only  for  embellishment,  will  be  excluded  ;  in  brief,  the  essential 
must  be  separate  from  the  unessential. 

As  belonging  to  the  unessential  will  always  be  reckoned,  firstly : 

'  All  harmonic  artificialities  (Kunsteleien)  in  general^  in  so  far  as  they 
are  founded  upon  no  inner  necessity  ;  unnatural  introduction  of  little- 
used  harmo7iies.  They  easily  produce  over-fullness,  swollen  over-loading  of 
the  passage,  and  bear  witness  rather  to  a  morbid  or  mentally  weak  condi- 
tion, than  to  originality  and  fresh,  free,  powerfully  secure  movement ; 
Then: 

Irregular  introduction  of  the  suspensions ;  the  use  of  stationary 
voicesj  and  of  the  anticipated  and  after-struck  tones  ; 

Especially,  however : 

The  changing  notes  which  are  struck  free  and  the  figures  formed  there- 
from ;  in  shorty  everything  which  appears  inappropriate  to  a  simple, 
good  four-voiced  song. 

If,  in  fact,  vocal  composition  is  received  as  the  basis  upon  which  all 
music  is  founded,  then  much  in  connection  with  it  will  of  itself  remain 
excluded,  which  is  appropriate  to  instrumental  compositions. 

If  also  for  practice  in  the  use  of  the  harmonies,  and  for  the  learning  of 
a  good  and  pure  leading  of  the  voices,  the  elaboration  of  chorals  or  simple 
movements  in  the  manner  of  chorals  is  directly  suggested  as  most  to  the 
purpose,  this  also  will  not  exclude  the  use  of  those  means  in  so  far  as  they 
serve  not  merely  for  embellishment  but  for  the  development  of  the  lead- 
ing of  the  voices. 


138  MANUAL    OF   HARMONY. 

Among  these  is  especially  to  be  reckoned  the  use  of  the  suspensions  and  of 
the  regular  passing  and  changing  notes. 

In  accordance  with  the  foregoing,  the  strictness  of  the  pure  harmonic  struc 
ture  in  connection  with  the  first  study  of  harmony,  and  later  contrapuntal 
labors  may  now  be  judged,  which  forbids  many  things  the  practice  likes 
to  use  in  appropriate  places,  as  not  to  the  purpose,  immaterial,  and  as 
causing  deviation  from  the  chief  object. 

The  thorough  study  of  good  compositions  will  serve  for  the  complete 
understanding  of  all  subjects  thus  far  discussed.  Chapter  XIX.  in  Part 
III  of  this  book,  in  which  we  return  to  this  subject,  will  afford  opportu- 
nity for  attempts  of  our  own. 


CHAPTER  XV. 


JPassing  Chords, 

Those  are  called  passing  chords,  which  in  smaller  parts  of  measures, 
after  the  manner  of  the  passing  notes  in  several  voices,  appear  as  actual 
chord-formations,  in  the  entrance  and  treatment  of  which,  however,  a 
manner  is  sometimes  found  deviating  from  the  general  rules  of  chord- 
connection. 

Of  these,  one  kind  has  appeared  already  in  such  passing  and  changing 
notes  in  three  voices,  as  take  on  the  chord  form,  e.  g.^  in  Nos.  271  and  272. 
Just  so,  the  most  of  the  chords  which  are  formed  over  an  organ-point  can 
in  a  certain  sense  be  called  passing  chords. 

There  are,  however,  still  other  phenomena  of  the  kind,  which  are  to  be 
here  explained. 

As,  in  general,  passing  and  changing  notes  depend  principally  upon  the 
relations  of  measure,  it  becomes  necessary  for  the  explanation  of  the 
passing  chords  to  cast  a  glance  at  the  various  division  of  measure. 

It  is  known,  that  in  the  simple,  even  varieties  of  measure^  the  natural 
accent  rests  upon  the  first  measural-division,  while  the  second  receives  a 
less  weight. 

If  now  the  harmonic  progression  be  based  simply  upon  the  two  measural- 
divisions,  then  the  harmonies,  which  come  upon  the  accented  division 
(Thesis)  will  always  appear  as  the  more  weighty,  and  must  alwaj;..  be 
conceived  of  as  the  goal  to  which  the  chords  of  the  second  divison  (Arsis; 
lead: 


MANUAL    OF    HARMONY, 


275. 


In  this  sense,  the  chords  of  the  second  measural-division  can  be  called 
passing  chords,  although  in  the  regular  movement  this  character  of  theirs 
does  not  appear  so  plainly. 

That  this  has  been  so  understood  in  the  theory,  even  if  seldom  plainly 
sxpressed,  is  shown  by  the  fact  that,  at  their  entrance,  more  care  has  ever 
been  bestowed  upon  the  chords  upon  the  thesis  ;  and  in  case  of  those  upon 
the  arsis,  much  has  been  allowed  which  was  not  conceded  to  the  former. 

The  character  of  the  passing  chords  appears,  however,  more  plainly  with 
such  harmonies  as  are  assigned  to  smaller  divisions  of  the  measure,  as  in 
the  following  examples  :  ^ 


2T6. 


6 
6       4 


7b 


2  7b 


m^^=\'^m=^^^^=l 


:F=tzt 


i^: 


_j__...^ 


1 


8 4 


np^ngn 


277. 


:J=d: 


mmn 


rr^- 


i 


§! 


mmm^ 


:f=!r- 


The  peculiar  manner  of  appearance  of  the  chord  of  the  sixth  and  fourth 
in  Example  No.  276  ci  and  c^  as  well  as  of  the  chord  of  the  seventh  in  c, 
is  only  to  be  explained  through  the  ensuing  progression  [in  the  character 


140 


MANUAL     OF   HARMONY. 


of  the  passing  notes)  of  all  voices^  hy  degrees ^  to  their  nearest  goal — the 
chord  of  the  thesis  in  the  following  measure. 

These  voices  can  be  still  more  easily  recognized  in  their  character  as 
passing,  if  one  voice  is  allowed  to  remain  stationary,  for  example,  the 
Bass  of  No.  277  a^  or  the  upper  voices  h,     (See  above,  No.  277). 

The  leading  of  the  voices  in  No.  276  a^  has  arisen  from  the  application 
of  both  modes. 

If  this  condition  (the  progression  of  the  voices  by  degrees)  is  fulfilled, 
then  all  chords  can  enter  free ;  they  will  find  explanation  in  the  principal 
chord  which  immediately  succeeds  them. 

NB  NB. 


37§. 


ii^fi^il 


ii 


111' 


— <5- 


F=t 


liii: 


Remark, — In  this  explanation  of  the  passing  chords,  the  free  treatment  of  the  seventh, 
mentioned  before,  finds  also  its  justification.     (See  NB.) 

In  the  simple  uneven  varieties  of  measure  the  accent  likewise  falls  upon 
the  first  measural-division,  whereas  they  contain  two  measural-divisions  of 
less  weight.    Passing  chords  will  show  themselves  in  the  following  manner : 


279. 


¥:       ^ 


■^Hkl 


64       2  6  7     6(2     987  24j8^756 


^m 


Smaller  measural-divisions  can  also  contain  passing  chords,  and  after  the 
above,  no  example  is  needed  for  it,  and  just  as  little  for  the  compound 
varieties  of  measure. 

Here  also  the  study  of  good  compositions  will  be  explanatory,  and  lead 
to  advancement. 

For  personal  attempts  the  following  remarks  may  still  find  place  : 

All  chords  designated  as  passing  will  either  progress  according  to  the 
known  rules  of  the  connection  of  harmony,  or  deviate  from  them.  In  the 
first  case,  which  is  more  frequent,  no  farther  remark  is  necessary  ;  in  the  last, 
it  will  depend  upon  a  flowing  melodic  leading  of  the  voices,  as  well  in  them- 


MANUAL    OF    HARMONY, 


141 


selves,  as  also  in  relation  to  each  other,  whether  formations  of  this  kind  arc 
to  be  called  correct.  It  can  only  be  remarked  in  general,  that  the  progression 
of  the  voices  hy  degrees  will  also  here  determine  the  character  of  the 
passing  chords,  and  that  all  such  passages  are  to  be  judged  after  taking 
into  account  the  rythm,  tempo  and  character  of  the  composition. 


CHAPTER    XVI. 


On  the  Means  for  3Iodulation, 

The  term  modulation  has  already  been  explained  in  Chapter  XI. 

There  the  object  was  to  determine  each  modulation  correctly ;  now  we 
are  to  treat  of  the  best  means  for  effecting  a  modulation. 

The  art  of  modulation  consists  in  finding  out  those  harmonies  which 
stand  in  connection  with  two  or  more  keys,  in  order,  by  means  of  these  to 
pass  from  one  key  into  the  other. 

Every  modulation  can  be  effected  in  various  ways,  and  will  serve  various 
purposes.     It  can, 

Firstly :  begin  abruptly,  be  quicMy  completed  and  pass  by,  or 

Secondly  :  be  more  gradually  prepared  for,  seek  out  the  new  key  as  a 
goal,  and  take  it  for  a  length  of  time  as  basis. 

In  the  first  case  it  will  avail  itself  of  the  simplest  means,  make  its  ap- 
pearance with  decision,  but  soon  leave  the  new  key,  and  perhaps,  indeed, 
not  allow  it  to  attain  to  a  definite  development  of  itself;  in  the  second  case 
it  is  commonly  prepared  and  worked  out  gradually  by  various  means,  and, 
endeavoring  to  impress  the  new  key  upon  the  ear,  will  probably  also  lead  to 
a  close. 

Thus,  in  the  following  example : 

I 


280. 


! 1— ^-^ — !_J — |_J      _J_-I— I_J_ 


1  I  t 

6 
4 


♦  U*:    6    4  5  6    2  6 


F:  V, 


G:    V. 


0:    I 


the  modulation  will  be  transient  and  frequently  changing,  without  forsak- 
ing materially  the  principal  key,  C-major. 


142 


MANUAL    OF   HARMOjs  r. 


Tliis  kind  of  modulation  is  only  adapted  for  the  nearest  related  keys, 
and  although  more  distant  ones  can  be  reached  by  especial  and  decided 
means^  still  in  their  development  very  natural  and  organic  combinations 
must  prevail,  if  they  are  not  to  appear  unintelligible. 

In  the  next  example,  however,  the  more  distant  key  becomes  the  goal, 
which  is  gradually  reached  ;  the  original  key  is  entirely  forsaken,  and  the 
new  one  takes  its  place  : 


291. 


pi^^^ii=i 


C:    I  b|):  vu^iy 


This  example  shows  plainly,  how  the  extended  modulation,  whicb  sets 
for  itself  the  new  key  as  goal,  makes  use  of  the  passing  modulation,  in 
order  to  reach  it,  and  this  the  rather,  as  it  was  not  the  object  to  reach  El? 
major  quickly. 

Unless  we  wish  to  use  such  short  passages  as  interlude  between  two 
compositions  of  different  keys,  or  as  exercises,  they  must  be  made  use  of  in 
composition  in  a  special  manner,  since  upon  the  formation  of  the  modula- 
tions themselves  rests,  in  part,  at  the  same  time,  the  formation  of  the 
periods  and  their  divisions.  This,  however,  is  an  important  part  of  the 
doctrine  of  Form,  and  belongs  to  the  arrangement  of  the  modulation  of  a 
composition,  and  is  thus  foreign  to  our  immediate  purpose. 

Remark. — An  elucidation  of  this  may  be  found  in  the  author's  work — "  Die  Grund- 
zuge  der  musikalischen  Formen  und  ihre  Analyse!!^ — (Leipsic,  G.  Wigand.) 

We  make  use  at  present  of  the  formation  of  such  modulations  as  exer- 
cises, in  order  thereby  to  promote  skill  in  the  use  of  the  harmonies  and 
their  appropriate  connection. 

While  the  means  for  modulation  are  being  searched  out,  no  immediate 
attention  will  be  paid  to  the  hind  of  modulation  used,  since  the  same  can 
serve  for  both  the  above  designated  kinds. 

The  first  and  simplest  means  will  be 

THE  TONIC  TRIAD  OF  THE  NEW  KEY 
itself. 

If,  however,  this  triad  is  already  a  component  part  of  the  first  key,  then 
what  succeeds  only,  and  particularly  the  subsequent  dominant  harmony  of 
the  new  key,  will  really  determine  the  intended  modulation.     Thus,  in  the 


JJU.I't  J^  ■'^  """^ 


MAX  UAL    OF    HARMONY. 


143 


following  example  at  a^  no  modulation  will  be  felt,  while  at  h  we  hear  the 
key  of  G-major  plainly  only  when  we  come  to  the  third  harmony  : 

a.  ^  *• 


In  ease  of  more  distant  keys  the  minor  triad  can,  to  be  sure,  as  tonic 
triad,  hare  a  more  decided  effect,  still  for  the  sake  of  definiteness  the  dom- 
inant harmony  will  succeed  it  (at  a)  /  the  major  triad,  however,  will 
incline  to  make  itself  understood  as  dominant  (&)• 


2§3. 


:i=Hg: 


'l^i~: 


M 


A  — O i._g 


i^l^ii^l^f^l^g 


C:   I 


C:  I 


111 
e:    I 


feHl^=^I^E^I!i=l 


As  tinsatisfying  as  the  tonic  triad  shows  itself  to  be,  for  modulation, 
in  the  way  used  above,  in  as  great  degree  has  one  of  its  inversions  (the 
chord  of  the  sixth  and  fourth)  the  quality  of  rendering  such  modulation 
particularly  decided.  For  just  as  it  naturally  takes  part  in  the  closing 
cadence  (see  pages  49  and  53),  so  it  produces  at  its  entrance  the 
feeling  of  a  modulation,  if  it  is  not  used  in  the  manner  of  the  passing 
chords,  but  enters  at  the  thesis.  However,  in  this  case  also,  it  is  naturally 
followed  by  the  dominant,  which  first  completes  the  modulation. 


284. 


6 

4     t 


^^mmi 


144  MANUAL    OF   HARMONY. 

Upon  the  arsis  it  will  not  indicate  the  key  so  definitely : 


2§5. 


6  G  7     r. 

4  71?  ^      4  I      4  Jf 


All  examples  given  above,  however,  point  to  a  still  more  potent  means 
of  modulation,  viz., 

THE    DOMINANT    HARMONY. 

The  triad,  as  well  as  the  chord  of  the  seventh  of  the  dominant,  shows 
itself  as  the  most  natural  and  best  means  of  digression,  since,  through  it, 
(which  applies  especially  to  the  dominant  harmony  of  the  seventh)  the  key 
is  most  unmistakably  determined  : 

The  modulation  through  the  chord  of  the  seventh  of  the  dominant  can 
be  effected  without  intermediate  chord  in  the  following  manner. 

According  to  the  principle  that  that  connection  of  harmony  will  be 
most  easily  comprehended,  which  is  effected  through  like  or  stationary 
tones  (preparation),  modulations  can  be  effected  through  the  dominant 
chord  of  the  seventh,  from  the  tonic  major  triad  into  all  remaining  keys, 
except  the  keys  of  the  minor  and  major  third,  and  that  of  the  augmented 
fourth.  From  C-major  we  can  reach  all  keys,  except  El?,  E  and  Fjf,  (it  can 
remain  undetermined  for  the  present  whether  major  or  minor)  thus  : 


From    C    to    d: 


F: 


F 


^^^=bf 


Everywhere  in  these  examples  the  like  tones,  which  are  connected  with 
each  other  by  a  tie,  mediate  the  transition  to  the  dominant  of  the  next 
key;  thus,  from  C  major  to  D  minor,  the  tones  G  and  E,  which  become 
fifth  and  seventh  of  the  dominant  harmony,  &c. 


MANUAL     OF    HARMONY.  145 

Remark. — It  only  need  be  mentioned,  that  these  modulation?  ^t.  also  be  reached 
through  other  positions  of  the  chords,  e.  g. 

C       —      d:  or:    ^^ 

287.    '        ^     ^       -       '      ^      -      ^      I 


If.  we  wish  to  modulate  in  the  same  manner  into  the  three  keys  which 
are  wanting  above,  it  can  be  done  by  means  of  an  inserted  chord  (in  the 
simplest  manner,  by  a  triad),  which  then  supplies  the  missing  connec- 
tion, e.  g. 

From    C  to  E^:  C  —  E:  C  —  Fjf: 


t2SS. 


pi^^-bSg^EE^^^l^ 


■*■—•■*•  Sir 


tf"  -    ||,r|* 


The  modulation  from  the  minor  can  be  formed  thus : 

From    AtoB:  A     —     d:  a        —        e:  a—        F: 


G: 


Si^     ^  "*^^Zi  -w-  -r^-       -f.^      -— 


oUr  „^:  fc._t_«._5ea_-^g — It 


*|-    - 


■^if-Ti- 


To  the  remaining  keys  C,  Dj?,  Ej?,  Fj(  and  A|?,  by  means  of  a  connecting 
chord  : 

From    A  to  C:  a  —  D^:  a  —  E{y; 


-»«•  feg&lif^3=l^^^=QEt^#EE 


FJ:  A  A\}'. 

5       ^^ 


^^^m^^mm. 


^  I- 

It  is  self  evident  that  this  manner  of  modulation  is  only  exhibited  as 
the  simplest  principle,  and  that  it  is  by  no  means  necessary  that  a  modu- 
lation should  always  take  place  in  this  way  ;  likewise,  that  as  simple  con- 
nections of  harmony  can  be  produced  without  a  stationary  tone,  so  also  can 
modulations ;  as,  for  example,  the  following  modulations  can  be  accomplished 
without  intermediate  chord : 


146  MANUAL    OF   HARMONY. 

From    C         to        Eij: 


.»..  $=mt~^^^^g^H^^^^ 


For  the  connection  of  harmonies  and  especially  of  the  keys,  it  will,  how- 
ever, always  be  of  great  use  to  make  ourselves  thoroughly  acquainted  with 
this  principle,  and  to  this  end  to  write  down  modulations  from  all  keys,  and 
therewith  to  bring  the  chords  into  the  most  various  positions,  as  also  to 
make  these  connections  evident  to  us  by  performance  upon  the  piano-forte. 

This  mechanical  proceeding  will  greatly  further  dexterity  in  the  use  of 
all  means  of  composition. 

Another  chord  shares  with  the  dominant  chord  of  the  seventh  the  capa- 
bility for  modulation,  viz., 

THE  CHORD  OF  THE  DIMINISHED  SEVENTH. 

This  chord,  which  in  most  cases  takes  the  place  of  the  dominant  har- 
mony, will  frequently  be  more  adapted  for  modulation  than  the  latter, 
Hince  its  entrance  is  much  milder,  particularly  in  those  cases  in  which 
seventh  and  fundamental  of  the  dominant  harmony  would  be  obliged  to 
enter  free  at  the  same  time. 

The  following  examples  present  the  use  of  this  chord : 

From    C     to     Bfe:  C       —      B:  C       —       d:  a     —     b: 


29i2. 


-mw^^^^^m^m^" 


Beside  this  application,  this  chord  shows,  by  means  of  its  enhannoniG 
nature,  a  farther,  peculiar  capability. 

The  following  chords,  entirely  like  as  to  sound,  but  variously  written : 


293.  i^gi^te^i^ 


belong  to  four  different  keys,  viz. :  in  the  first  form  to  F  minor,  m 
the  second  to  D  minor,  in  the  third  to  B  minor,  in  the  fourth  to  A{? 
minor. 

Through  this  circumstance  a  fourfold  modulation  is  possible : 

From    0   to     r:  C     —    d:  C    —    b:  C      —       a^: 

-  |l^i^^li|pifi|^|lf 

Since  now  all  the  chords  of  the  diminished  seventh  can  appear  in  the 
following  three  positions,  as  the  piano-forte  shows  most  plainly, 


MANUAL     OF   HARMONY.  U7 


295.         _ 

and  each  of  them,  through  enharmonic  interchange,  will  belong  to  four 
keys,  modulations  present  themselves  for  all  twelve  keys  in  minor,  to 
which  in  many  cases  we  can  add  the  twelve  in  major,  since  this  chord  can 
often  be  used  instead  of  the  dominant  harmony  in  major. 

Here  also  the  industrious  writing  down  of  this  manner  of  modulation 
will  tend  greatly  to  advancement  in  the  comprehension  of  the  inner 
connection  of  all  keys,  as  well  as  of  the  multiplicity  of  harmonic  con- 
nection. 

Although  this  manner  of  modulation  shows  itself  to  be  adapted  to  mani- 
fold uses  in  actual  composition,  still  it  must  be  remarked  that  it  should  not 
be  used  too  often,  since,  being  applied  lightly,  its  artistic  worth  becomes 
less. 

A  similar  application,  though  not  in  so  comprehensive  a  manner,  is 
exhibited  by 

THE  AUGMENTED  CHORD  OF  THE  SIXTH  AND  FIFTH. 

Its  similarity  as  regards  sound,  to  the  dominant  chord  of  the  seventh 

with  enharmonic  change,  adapts  it,  in  connection  with  the  latter,  for  mod- 
ulation into  certain  keys,  e.  g. 

From  C      to      b:  E{y     — -     d: 


297. 


pms^m^^m^^mm 


77 
C:    V^    b:  iio^        i  V         i         K2:  V^    d:  11°^  i     V 


Although,  in  the  above,  the  means  were  sought  out  with  which  to  pass 
quickly  from  one  key  into  the  other,  still  (since  it  will  not  always  be  the 
intention  to  carry  out  a  modulation  quickly  and  decidedly),  for  the  fur- 
therance of  skill  the  exercises  can  be  extended  and  given  out  in  the 
following  manner : 

From  one  key  into  the  other  hy  means  of  the  triads  of  various  d£gre€s . 

From  C  to  D  through  the  i^riad  of  the  third  degree : 


298. 


-^^m^¥- 


From  C  to  D  through  the  triad 


148  MANUAL    OF   HARMONY. 

Of  the  fourth  degree :  Of  the  fifth  degree :  Of  the  sixth  degret  : 


\ 


299. 


=f 


id=z|: 


=s=^g^^^^ 


ny-     ->,-     — 


iri 


cy  </ie  seventh  degree  : 


1 


From  C  major  to  E  through  the  triad 

Of  the  second  degree :  Of  the  fourth  degree : 

300.  ^Ei 


Of  the  fifth  degre^i: 


^ 


=3 


^     1^        77 


f 


i 


cy  i/ifl  «ia5f7i  degree : 


Of  the  seventh  degree : 


bj^fEipEis^l 


These  indications  may  suffice  for  learning  to  form  other  modulations 
according  to  the  same  principles. 

Extension   of  Modulation  and  its   Completion  throiigh  the 

Cadence, 

The  process  shown  above,  for  passing  from  one  key  into  the  other, 
was  based  upon  the  simplest  and  most  natural  means. 

If  we  wish  to  carry  out  more  at  length  a  digression  into  a  new  key,  the 
above  means  must,  to  be  sure,  serve  to  this  end,  they  are  not  however  applied 
so  suddenly  and  directly,  but  the  before  mentioned  passing  modulation  is 
used,  and  the  new  key  introduced  only  gradually.  The  use  of  the  cadence- 
formula3  will,  however,  establish  the  ultimate  key  in  the  best  manner. 

To  this  end  we  can  form  for  ourselves  the  following  kind  of  problems,  e.  g. 

Let  a  modulation  be  made  from  C  major  through  d  minor,  a  minor, 
and  Gc  major  to  e  minor. 

This  problem  would  be  solved  something  in  this  manner : 

301. 


^}i^^^^^mmmm^\w^mi 


C:     I  d:  viiO. 


a:  viiOf 


G:V. 


k:V, 


MANUAL    OF    HARMONY. 


140 


In  connection  with  the  addition  of  the  cadence,  the  following  is  to  be 
observed : 

If  the  modulation  takes  place  through  the  chord  of  the  sixth  and  fourth 
of  the  tonic  triad  of  the  new  key  (see  page  143),  then  the  succession  of 
the  dominant  chord  with  its  natural  progression  will  be  sufficient  f^r 
effecting  the  cadence,  c.  </. 


302. 


:=r^=^^U 


^|jE^|^=[i 


In  other  cases  the  extended  cadence^  or  the  known  closing  formulae  will 
be  requisite  (see  page  40)  in  order  to  determine  the  final  key.  As  the 
simplest  of  such  closing  formulae  the  following  are  commonly  used  : 


Jn  other  poiitiont : 


303. 


J J-r-    I        J    ,      — ;rr--j— '-r-l H-r ir 

i^-gi=:JizE:fi=:gzf:^=zit:^EE3ziEg=g=iE^i^IE 

0  6 

6         4         7  6         4         7 


^i-^ffi 


:d=T 


—a- 


i 


^mm^immm^^^mi 


In  other  positions . 


If  these  3adence-formula3  be  added  to  the  modulation  itself,  according 
to  the  position  of  the  last  chord,  then  it  is  completed. 

This  may  be  shown  in  connection  with  some  former  examples. 

The  modulation  from  C  to  Ej?,  No.  288,  closes  with  the  fifth  in  the 
Soprano.  To  this  is  added  the  cadence  in  the  position  which  answers  to 
this  last  chord,  e.  g. 


150 


MANUAL    OF   HARMONY. 


304. 


From  C  to  i^ :  Cadence  : 

-I ^-.— !■ 


3s^i^li^S-«i=j^Ei=fi 


b         tl 


5!>       6  41)       71) 


:^^==l 
f? 


EE=^^ig=lE^ 


d2. 


11 


The  following  modulation  from  C   to  a  in  No.  286,  would  require  a 
cadence  in  this  position  : 


From  C  to  A  : 


Cadence . 


305. 


=!::f=:i: 


Hiiiiliiilli^l 


f 

3 


•*^      Si- 

0 

4         « 


-^- 


^^^^^^^^^ 


'TJie  modulation  from  C  to  B  with  use  of  the  cadence  under  No.  303  b  •* 

From  C  to  B:  Cadence: 


306. 


Si^i^i§|i:Wi«^^ 


or  from  0  to 


307. 


Cadence  : 


Impi^pi^M^fE 


4b 
6      3ir 


5ir 


B^^^^^^^M^^ 


To  close,  we  present  an  example  of  a  more  extended  problem  : 

From  G  through  e  minor,        C  major,  and  BJ^  minor  to    Ajy  major.       Cadence: 

^ ^-,_J 1-_, 1 l-^—J -J  - 

5— fc^-Th-d— rH— f — 


30§. 


;^iEfe^ifeliiii^fe^EMpglE 


ife; 


i^ 


3^s==g 


^3= 


These  indications  will  be  sufl&cient  to  enable  us  to  form  for  ourse^ 
manifold  problems. 


MANUAL    OF    HARMONY,  161 


PART    III. 

PRACTICAL  APPLICATION  OF  THE  HARMONIES.— THE  EXERCISER 
IN  THEIR  USE  IN  THE  PURE  HARMONIC  STRUCTURE. 

Through  the  following  hints  respecting  the  manner  most  to  the  purpose 
in  the  use  of  the  harmonies,  the  principles  until  now  developed  will  be,  at  the^ 
same  time,  still  more  exactly  explained,   extended,  and   made  complete. 
To  this  end,  individual  cases  will  furnish  opportunity  for  farther  remarks. 

CHAPTER  XYII. 

The  Simply  Har^nonic  Accofnpanhnent  to  a  Given  Voice. 

It  may  first  be  remarked,  that  here,  only  simply  melodic  progression  ol 
a  voice  will  be  discussed ;  all  other  elements  of  a  melody,  as,  for  exam- 
ple, its  metrical  and  rythmical  development,  will  be  for  the  present 
excluded. 

1.  Harmonic  accompaniment  to  a  Soprano. 

We  select  the  following  simple  exercise  : 


30».  ^:^EgEE|^|gE|^|^|^lP 


To  facilitate  the  work,  those  fundamental  tones,  which  can  serve  as  the 
harmonic  foundation,  will  be  added  in  the  manner  used  before. 

c  G  c  i>  G  c 

With  every  harmonic  progression^  the  leading  of  the  Bass  is  the  most 
important  point. 

We  turn  our  attention  therefore  first  to  this,  and  write  its  progression, 
perhaps,  in  tne  following  manner  : 


V 


162 


311. 

SOPKANO. 

Babs. 


MANUAL    OF   HARMONY 

C  G  C  n  G 


C  n 


P-^ 


^11=1=1^^1111 


9iE^^;:: 


im^f^ 


er  in  the  following  way  : 

312.  9iEI$Eis: 


The  addition  of  the  middle  voices  will  now  present  no  difficulties 
313.      /[J  G  c  D  G  c 

—  pif^^l=l^l^lll[| 


Alto. 


Tknob. 


Bass. 


,_^__«_-__«. 


.,       .      -g^ — -r— »— |— ey — J — — -, — jy — Y'^ — rr 

Siillifliillililii 


Let  this  working  out  of  the  exercise  serve,  for  the  present,  for  the  expla- 
nation of  the  exercises  themselves. 

The  next  exercises  will  give  opportunity  for  becoming  acquainted  with 
the  principles  of  a  good  leading  of  the  Bass,  as  well  as  of  melodic  voices 
in  general  so  far  as  the  simplest  harmonic  progression  requires. 

Examples  worked  out  in  a  faulty  manner  can  best  serve  this  end. 

Exercise  with  indication  of  the  fundamentals : 


314. 


•^m^lii=l^iilll[^ 


Remaek. — la  the  treatment  of  this  and  the  following  examples  we  use  the  vioHo 
«lef  for  the  sake  of  saving  room,  and  write  the  voices  together  on  two  staves  ;  for  the 
personal  work  of  the  pupil,  however,  we  recommend,  mest  earnestly,  the  manner  of  no 
tatioQ  used  in  No.  813. 


The  working  out  of  this  exercise  may  be  as  follows 


MANUAL    OF   HARMONY. 


163 


315. 


m^^l^l^^mim 


zis: 


fiispj=j=ipgigE(| 


There  appears  nowhere  in  this  example  a  transgression  of  any  rule  of 
progression  and  chord-connection  thus  far  known,  and  still,  on  account  oi 
the  stiff,  uncertain,  and  powerless  Bass,  it  is  to  be  rejected  entirely. 

Except  in  the  case  of  the  organ-point^  a  good  harmonic  leading  of  the 
Bass  allows  it  to  remain  stationary  only  if  its  continuity  is  conditioned 
by  necessary  preparation  of  a  tone,  or  compensated  for  by  a  decided  pro- 
gression of  the  other  voices. 

The  previous  example  also  contains  the  chord  of  the  sixth  and  fourth 
twice,  which  may  give  us  opportunity  to  add  what  is  farther  necessary  con- 
cerning the  use  of  this  peculiar  and  difficult  chord.  /    ff  v^y/*  • 

'X^  Of  the  Use  of  the  Chord  of  the  Sixth  and  Fourth^n^y/ 

The  rare  use  of  the  second  inversion  of  the  triad,  the  chord  of  th  C( 
sixth  and  fourth,  has  its  reason  in  this,  that  its  appearance  depends  upon^^-^ 
certain  conditions. 

First,  we  find  it  oftenest  in  connection  with  the  cadence  formations,  as     ^ 
former  examples  show. 

Then,  it  appears  in  a  like  character  in  connection  tvith  modulation.  "* 
(See  page  143). 

It  can  probably  also  enter  free  in  both  cases,  it  must  then,  however,  be 
regarded  not  as  a  passing  chord,  but  always  appear  upon  the  thesis.-^.^ 

Except  in  these  cases,  it  appears  most  naturally  as  tonic,  dominant,  or 
sub-dominant  triad,  under  the  following  conditions  : 

a.     If  the  fourth  is  prepared  ;  ,s. 
X  |>,     J/  the  Bass  progresses  by  degrees  to  the  following  new  chord,  or 
remains  stationary  . 

The  following  examples  show  the  application  : 


316. 


6        6 
4       6 


154 


MANUAL    OF   HARMONY, 


fr=.x='- 


6        6 
4       6 


mmmim^^^ 


In  the  Examples  at  a^  it  appears  most  naturally,  because  it  rests  upon 
tonic,  dominant  and  sub-dominant,  while  upon  other  degrees  (&)  it  easily 
produces  the  feeling  of  a  modulation. 

Used  upon  the  arsis  (beside  appearing  under  the  above  conditions),  it  can 
also  appear  with  preparation  of  the  Bass. 


|i_lli:-i=i 


317. 


The  chord  of  the  sixth  and  fourth  shows  itself  in  all  these  examples, 
either  as  passing  chord  (upon  the  arsis),  or,  as  above,  in  the  character  of  the 
suspension  upon  the  thesis  ;  with  preparation  of  the  Bass  upon  the  thesis, 
it  appears  much  weaker. 

"Ipilii^iiippl^ 


31S. 


Not  unfrequently  it  will  appear   as  itself  a  suspension,  whereby  the 
preparation  of  the  fourth  i^  perfectly  justified,    v 


319. 


MANUAL    OF    HARMONY. 


155 


Iq  the  second  case  still  more  decidedly,  because  it  arises  with  a  rarely 
occurring  chord  (that  of  the  third  degree). 

That  the  chord  of  the  sixth  and  fourth,  however,  can  also  enter  free  in 
connection  with  a  leading,  by  degrees,  of  the  voices  of  smaller  measural- 
divisions,  in  passing,  as : 


320. 


s^^^ 


6 
4- 


P=E^g^=[E 


will  require  no  farther  explanation  after  what  was  said  in  Chapter  XV.,  of 
the  passing  chords,  and  after  the  examples,  Nos.  276,  279. 

Remark. — The  often  necessary  preparation  of  the  perfect  fourth  in  the  chord  of  tlie 
sixth  and  fourth,  has  led  many  theorists  to  reckon  it  among  the  dissonances. 

In  the  introduction  to  this  system  of  harmony,  in  the  division  of  the  intervals  (page 
16),  it  is  introduced  among  the  consonances;  and  also  (page  20)  the  reason  of  this  view  is 
given.  ■>,  ■  ,A^  ^  ■     f''  ■;,  .  y/  I  , 

The  doubtful  relation  of  the  perfect  fourth,  and  the  necessity  of  its  preparation  occurs 
only  over  against  the  JBass,  or  the  lowest  voice,  and,  in  fact,  in  the  chord  of  the  sixth 
and  fourth  only,  since  in  the  chord  of  the  sixth,  fourth  and  third,  itself,  this  necessity  of 
preparation  is  not  always  found ;  between  the  other  voices  the  perfect  fourth  is  to  be 
treated  just  as  any  other  consonance. 

With  the  real  dissonances  this  is  not  the  case,  for  these  retain  their  character  every- 
where, whether  they  appear  above,  below,  or  in  the  middle. 

The  chord  of  the  sixth  and  fourth  of  the  diminished  triad  will  seldom 
be  appropriate  for  use  four-voiced,  because  it  appears  too  incomplete. 


321. 


On  the  other  hand,  it  will  occur  in  three-voiced  composition,  where  it 
often  takes  the  place  of  the  chord  of  the  second.  (See  later,  the  three- 
voiced  movement). 

Besides  the  condition  of  a  good  harmonic  progression,  viz.,  that  the  Baw 
itself  should  form  a  good  and  intelligible  foundation  for  it,  the  second 
requirement  is, 

THAT  THE  PROGRESSION  SHOULD  ALSO  BV,  MELODIC. 


ir,6 


MANUAL    OF   HARMONY. 


Among  the  unmelodio  progressions  have  always  been  rightly  reckoned 
certain  skips. 

The  succession  of  two  fourths  and  fifths  in  the  same  direction,  e.  a. 


322.  p: 


lUPlll 


These  skips  are  improved  thus : 

g-"   J :3_« C — f^-. — I _I»i2 L 


— s- 


-C?^ 


i  i 


Even  skips  of  a  sixth,  if  the  situation  and  compass  of  the  voices  admita 
of  it,  are  better  carried  out  by  skips  of  a  third  in  a  contrary  movement : 

tetter :  tetter  : 


»S84.  ^j=.- 


;^iif; 


m 


Augmented  interval-steps  and  skips  are  to  he  avoided  as  unmelodic ; 
diminished  are,  however,  good. 

not :  better : 

325.  g^ 


not :  tetter  :  not : 


i^li^^^^i^ 


not: 


^= 


fI- 


tetter: 


not: 


better: 


11 fi- 


i 


#= 


r|=: 


:i^ 


--^ 


Deviations  from  this  rule  are  often  found ;  they  find  their  explanation  in 
A  formation  of  melody,  or  in  the  especial  character  of  the  composition  as  a 
whole.  The  observance  of  the  rule  in  theoretical  labors  will  always  be 
very  improving. 

The  skip  into  the  major  seventh  is  to  he  entirely  avoided;  that  into 
the  minor  seventh  can  he  used,  hut  only  in  case  of  an  inversion  of  the 
same  chord. 


not: 


not: 

.(5- 


»*«•  ii=^^E§==PE=iE 


i 


i?^ 


If 


The  last,  perhaps,  with  the  following  progression  of  harmony : 


327, 


not  very  good 

'       not: 

not: 

m^ 

—G>— 

G- 

EE^ 

:^:=:(fe 

^-^ 

-^ 

^W- 

~^w- 

-If 

mi 

~a:z 

.^.. 

6 

— r-©~ 

i^^ 

l\^. 

ba- 

-^^- 

or- 

ill 

MANUAL     OF    HARMONY. 


15: 


These  few  observations  contain  the  principal  features  of  a  good 
melodic  leading  of  the  voices,  and  especially  for  the  next  (simply  harmonic) 
exercises,  prove  themselves  sufficient.  It  should  still  be  remarked,  that 
these  rules  apply,  not  alone  for  the  leading  of  the  Bass,  but  in  general  for 
all  voices. 

The  exercise  given  under  No.  814  can,  -with  an  improved  progression  of 
the  Bass,  be  worked  out  something  in  this  manner  : 


32§. 


iPpppiiigiipipB 

-2 


8      7 


giE^E^lEg^l 


^1 


32§d. 


'M. 


"^ 


a  -■ ^ 


Exercises, 


-r-O- 


£EE^ 


C  — 


m 


F  C         G 

3. 


S^l=l^ 


|3=^ 


m 


C         Qt 


c       ©Y 

15: 


illimi^^ii 


The  next  example  will  give  occasion  for  the  explanation  of  an  impor* 
tant  and  difficult  part  of  harmonic  connection  and  leading  of  voices. 


329. 


Exercise, 

bO  C  A 


Diy  Gy 


3^=^f=s=:|-g=|-g=|=^ 


i 


The  following  faulty  work  may  serve  for  illustration : 


"T  o? 


330. 


■-w=^ 


iiE^i 


-^■ 


C_<5 (2- 


6       7 
5 


158 


MANUAL    OF    HARMONY. 


The  faults  of  this  treatment  of  the  exercise  consist,  firstly,  in  the 
doubling  of  the  third  of  the  second  chord  through  the  Bass,  which,  with- 
out occasion,  gives  to  this  and  the  following  harmony  an  awkward  position  ; 
secondly,  in  the  indicated  covered  fifth  (from  the  fourth  to  the  fifth  measure), 
and  lastly,  in  the  introduction  of  the  seventh  by  a  skip,  in  the  next  to  the 
last  measure. 

As  concerns  the  last,  this  can  take  place  with  the  dominant  seventh 
only — the  fundamental  being  already  present  (prepared).      (See  page  70). 


331. 


More  tolerable  and  less  harsh  is  the  free  entrance  of  the  seventh,  and  of 
the  fundamental  in  contrary  motion  ; 

-g o — FF 


332. 


m parallel motion^hovf e\er^\t  is  either  to  be  rejected  entirely,  or  only  applied 
in  connection  with  especially  favorable  progressions,  if,  perhaps,  as  in  the 
first  example  of  No.  333,  the  fundamental  (G)  is  already  present  in  the 
previous  chord,  although  in  another  voice. 


333.  feziz 


i 


czzis: 


l=li 


The  first  of  the  faults  instanced  above  will  be  corrected  in  what  follows. 
The  second  is  more  important,  and  will  give  us  occasion  to  speak  in 
general 

OF  COVERED  FIFTH  AND  OCTAVE  PROGRESSIONS. 

The  nature  of  these  progressions  has  already  been  spoken  of,  page  29. 

Covered  fifths  and  octaves  arise,  if  two  voices^  starting  with  different 
intervals,  progress  in  parallel  motion  to  an  octave  or  fifth,  e.  g. 


334. 


Covered  fifths ; 


-s- 


f=::r^z2zi:=-:Sirszrp; 


1= 


i 


:i:: 


Covered  octavet 


MANUAL     OF   HARMONY,  159 

These  fifths  and  octaves  become  open,  if  the  skip  which  one  or  both 
voices  make,  be  filled  out  by  the  tones  which  lie  between,  as  is  indicated 
above  by  the  points. 

Since  in  every  four-voiced  movement  certain  covered  fifths  and  octaves 
can  occur,  without  which  the  choice  of  chords,  as  well  as  the  leading 
of  the  voices,  would  be  very  much  limited,  and  also,  since  others  are  to 
be  avoided,  it  becomes  necessary  to  take  a  somewhat  nearer  view  of 
the  manner  of  their  appearance.  An  attempt  to  give  positive  rules  for 
their  use,  which  would  be  sufficient  for  all  cases,  has  not  yet  been  success- 
ful, and  would  probably  with  great  difficulty  succeed  ;  there  are,  therefore, 
only  general  observations  to  be  made,  which,  however,  will  furnish  a  stan- 
dard  of  criticism  for  especial  cases. 

Covered  fifths  and  octaves  between  two  voices  can  occur : 

1.  If  one  voice  moves  hy  a  step  and  the  other  skips  ; 

2.  If  hoth  voices  skip. 
In  the  first  case : 

a.     By  a  step  in  the  upper,  and  a  skip  in  the  lower  voice; 

h.     By  a  skip  in  the  upper,  and  a  step  in  the  lower  voice. 

In  regard  to  both  cases  as  concerns  the  kind  of  voices  : 

a*     Between  the  outer  voices, 

h.     Between  the  middle  voices,  and 

C.     Between  an  outer  and  a  middle  voice. 

Covered  Fifths  and  Octaves  in  the  Outer  Voices,* 

They  are  to  be  allowed,  if  the  upper  voice  progresses  hy  a  step. 
Fifths:  h.  c.    Octaves:      d.  e. 


335. 


Here  it  is  well,  if  one  voice  be  at  the  same  time  led  in  the  contrary 
movement  or  remain  stationary,  as  in  Example  No.  335  a^  1)^  C,  It  is 
not  so  well,  if  all  voices  go  in  parallel  motion  {d). 

Remark. — Although  the  above  rule  will  suffice  in  so  many  cases,  still  it  cannot  always 
apply,  as  the  above  Example,  No.  335  rZ,  shows,  which  is  not  to  be  reckoned  among 
those  which  exhibit  a  first  rate  leading  of  the  voices,  since  the  progression  from  the 
chord  of  the  sixth,  c,  is  a  very  forced  one. 

We  must  remember  also,  what  has    been  said  before  concerning  the  cadencing  pro- 
gi-ession  of  the  Bass,  pages  35    and  36,  viz.,  that  covered  octaves  which  pass  over  the 
leading  tone,  or  in  general,  over    the  half-step,  are  always  more  tolerable  than  those 
rhich  pass  over  the  whole-step. 


160 


MANUAL    OF    HARMONY. 


In  the  exercises  exhibited  above,  the  octave  always  shows  itself  aa 
fundamental  of  the  chord ;  cases  in  which  it  forms  the  third  of  the  chord 
are  much  more  questionable,  and  therefore  to  be  used  more  cautiously. 


not. 


not: 


336. 


pp=«3:-|=i 


Even  as  fifth  of  the  chord  it  is  not  to  be  called  good. 


337. 


:^ 


-G- 
•77 


/ 


Remark. — With  the  covered  fifth,  the  lower  voice  will  always  be  the  fundamental  of 
tiie  chord. 

fiovered  fifths  in  the  outer  voices  are  to  he  rejected  if  the  upper  voice 
skips, 

h.  e.  d.  e. 


33§. 


iwim^^^^^^i 


^^!^| 


fiifji; 


I 


XWherever  a  seventh  makes  the  connection  of   the  harmony  firmer,  as 
/at  Of  df  Cf  the  progression  of  fifths  appears  more  covered  and  less  harsh. 
Covered  octaves  in  the  outer  voices  are  not  to  he  unconditionally  rejected 
if  the  upper  voice  skips. 


339. 


b,    not .' 


d.    not : 


m^^MM^^i^^^^^t^^l 


6 


•^>v«^ 


i^HE^-MliTMHiMflllMi 


Here  also  those  cases  in  which  the  Bass  progresses  a  half-step  (a)  show 
themselves  to  be  most  tolerable.  What  was  said  in  connection  with  Nos 
336  and  337  applies  for  d  and  e» 

Covered  fifths  and  octaves  in  the  outer  voices  are  to  he  rejected  ifhoth 
voices  skip. 


MANUAL    OF    HARMONY 


;:.io. 


y  If,  however,  they  only  form  inversions  of  the  same  chord,  they  are  not 
to  be  considered  as  faults,  since  in  that  case  they  are  not  progressing  fiftha 
and  octaves  at  all. 


341. 


11131^ 


— -s 


w 


iiiHilii^lim^lE 


Covered  Fifths  and  Octaves  in  the  Middle  Voices, 

Although  the  leading  of  the  middle  voices  must  be  just  as  pure  aa 
that  of  the  outer,  still  their  situation,  which  is  much  covered  by  the  latter, 
allows  them  occasionally  a  greater  freedom ;  this  particularly  applies  to 
tlic  covered  fifths.  Covered  octaves  are,  here,  if  only  for  the  sake  of  the 
good  relation  of  the  voices,  not  to  be  called  good ;  with  respect  to  the 
covered  fifths,  aside  from  the  above  observations,  all  will  immediately 
depend  upon  an  otherwise  good  connection  of  harmony.  A  few  cases  may 
have  place  here  : 


not : 


Slt2. 


i^iP^3ilil3ii^^^l^^ 


■-t^ 


li^il^^l^^^^j^j^l 


1  \ 


— o- 


i: 


te--?ps: 


Covered  Fifths  and  Octaves  between  the  Outer  and  3Iiddle 

Voices, 

The  considerations  which  are  to  be  taken  into  account  in  connection  with 
these  progressions  of  the  voices,  are  to  be  sought  in  a  good  and  natural 


162 


MANUAL     OF   HARMONY, 


connection  of  harmony,  rather  than  established  through  merely  mechani- 
cal  rules.     Here  are  some  examples  : 


34S. 


I 


'^l^i^l 


I 


i?=i=:gziiz^$ii=T-^ 


f^ 


^^i^m^mm^^m 


not  good: 


not: 


S;_ 


^s^ni^f 


m= 


—  "~  ■»  <5  ^ 


;i^r=^^^l^lii[| 


f       An  especial  kind  of  covered  octaves  is  still  to  be  mentioned,  viz.,  such 
as  pass  over  the  seventh  ;  these,  in  all  voices,  are  to  be  avoided  as  faulty. 


344. 


'^m 


i^-^iaiiiiiiMf 


(See  page  84.) 


That  which  was  remarked  of  the  octaves,  applies  also  to  covered  unisons. 
Between  Soprano,  Alto  and  Tenor,  the  latter  are  to  be  avoided  entirely, 
between  Tenor  and  Bass,  however,  they  are  to  be  regarded  as  covered 
octaves — according  to  the  postion  of  the  chord  and  of  the  voices  themselves. 

The  cases,  in  which  covered  fifths  and  octaves  can  appear,  are  so  man- 
ifold; that  it  would  be  superfluous,  if  it  were,  in  fact,  possible,  to  adduce 
them  all.  The  above  observations  may  suffice,  if  we  add  the  following 
maxim,  which,  to  be  sure,  is  not  written  for  those  beginners  who .  still 
have  to  do  with  the  technical,  or  the  properly  mechanically-harmonic 
structure,  without  regarding  the   higher  requirements  of  art : 

Avoid,  indeed,  covered  fifths  and  octaves  as  much  as  j^ossihle  ;  consider 
ihem^  however,  as  safe  if  on  the  one  hand,  an  otherwise  natural,  good  con- 
Election  of  harmony  takes  2^lctce,  or  on  the  other,  considerations  of  a  higher 
aort  prevail;  such  as  melodic  voice-movement,  application  of  defimite 
motives,  etc.  " 


MANVAL    OF   HARMONY. 


lC?i 


After  this  digression,  we  return  to  No.  330,  in  order  to  correct  the  before- 
mentioned  fault. 

A  correction  of  the  covered  fifth  found  there,  which  belongs  in  that 
category  where  both  voices  skip,  will  be  hardly  possible  in  this  case, 
because,  even  if  the  Bass-progression  proceed  in  the  contrary  movement, 
the  evil  presents  itself  again  in  another  place,  e.  g. 


345.    / 


l-ilil 


iiliMa 


Thus  it  only  remains  to  alter,  in  this  case,  the  harmony  itself,  and  select 
another  marking  of  the  fundamental  tones. 
The  following  alteration  can  take  place  : 


346. 


or ; 


347. 


bO 


Dij-         G^ 


s^^^^ 


-^ 


i 


6 

5  8       7 


i::^: 


EEE 


^^l 


bO 


P7 


^ 


'-W 


^^^^ 


its: 


I 


347  ft.  =rk(pps= 


2. 

— — -^— yfc- 


Exercises, 


ZZSZZ  ZZ^^I  T, 


Hil^ 


F  Bb  kO  F  D  G^       C^       F 


164 


MANUAL    OF   HARMONY, 


348 


The  following  exercise  : 
G        c        o 

I 


m 


Dy         G  C  G 


il 


we  will  work  out  in  this  manner : 

1.  2. 


S4i). 


I 


3. 


4.       5. 


^^^H^^i^l^ 


"#■" 


■.«ar-  g.-^:^^ 


6  6 

4  5 


§ife 


t   I    ^ 

8    7 


i 


lis: 


l^PiE 


The  faults  of  this  work  are  indicated  by  figures. 

The  movement  of  all  the  upper  three  Toices,  by  skips  in  parallel  motion, 
at  No.  1,  is  not  good,  since  it  ofiends  against  the  first  principles  of  all  har- 
monic connection  and  is  by  no  means  necessary. 

A  leading  of  one  or  two  voices^  hy  skipsj  can  take  place  only  if  through 
a  third  voice  (by  a  tone  remaining  stationary  or  by  a  contrary  motion),  the 
harmonic  connection  is  preserved. 

No.  2  also  contains  the  same  fault,  which  here  becomes  still  harsher 
because  seventh  and  fundamental  enter  free  and  come  thereby  into  an 
awkward  position,  so  that  one  is  crowded  by  the  other. 

It  has  already  been  mentioned  (pages  72  and  158),  that  the  free  entrance 
of  the  seventh  can  take  only  place  without  harshness,  if  the  fundamental 
is  already  present,  and  can  remain  stationary  in  the  same  voice. 

Thus,  none  of  the  following  examples  exhibit  a  superior  leading  of  the 
voices. 


350. 


i^ssiisgggi^^gsi 


__^,j§-_.j^  _^__j^r^^_^_^^|2a__j?L.^:^__^ 


@eiysiii[i§uimiifitiiE 


I 


MANUAL    OF   HARMONY. 


165 


Probably  few  of  these  and  similajr  instances  would  be  excusable  for 
more  important  melodic  reasons. 

The  following  examples  may  still  serve  as  completion  of  the  free  intro- 
duction of  the  fundamental  and  the  seventh  in  contrary  motion,  mentioned 
on  page  158. 


351. 


._fi_,_-^_,_-^_,-l2g-:r-_^_,-j*^2-^fc 


^^mm-^\^^\mi 


The  instance  No.  2,  of  Example  No.  349,  contains  besides  this,  another 
fault,  contrary  to  the  rule  laid  down  above  (page  153),  in  connection  with 
the  chord  of  the  sixth  and  fourth,  viz.,  that  the  Bass  should  not  skip  from 
the  chord  of  the  sixth  and  fourth. 

The  third  fault  of  Example  No.  349  consists  in  the  covered  fifth,  which 
is  the  more  prominent  in  connection  with  the  skip  of  the  Soprano  in  the 
same  direction,  as  well  as  in  the  general  scattered  leading  of  the  voices. 

The  covered  fifth  in  No.  4  is  to  be  condemned,  on  the  ground  that  it  was 
tot  necessary ;  that  at  No.  5  is  better ;  it  can  take  place  in  connection 
with  the  leading  of  the  Alto,  as  well  as  of  the  Bass  in  contrary  motion. 

The  following  will  be  a  better  working  out  of  Exercise  No.  348. 


I,   ( 


352. 


ifElEi 


5: 


EE: 


im^ 


^Me^^ 


^   ^   ±r  .sj   ^ 


6         6         2 
4 


8     7 


«— r-^ 


Eocercises, 


352. 


•^•ii&=l 


^ 


«— r-«- 


T^P 


Ttsu::. 


i 


GC         —         G         —         D  aDGD, 


T— ©— T 


E?EI^5^ 


r=iPJ^i^i^i^Ei 


C  D. 


^7 


166 


MANUAL     OF   HARMONY. 


4. 


P 


t^- 


^_       C—    -42— T-©. 


^i==1 


_«_, 


^; 


The  next  exercise^ 


FttO 


353. 


■*"7 


i 


with  the  followiDg  treatment : 


354. 


i 


•'4>^g — -- 1 1~" 


^^11 


iQz::: 


iGiii 


^.^..p. 


^[fi 


•rv^^ 


gives  us  opportunity  to  speak  of  a  fault  which  bears  the  name, 
UNHARMONIC    CROSS-RELATIO]!^. 

The  unharmonic  cross-relation  (relatio  non  harmonica)  belongs  to  the 
unmelodic  progressions,  and  consists  in  general  in  this ;  ihat  upon  one  tone 
immediately  follows  the  same  tone  in  another  voice,  chromatically  raised 
or  depressed^  as  here  upon  the  Gr  of  the  Alto  the  GJ(  of  the  Bass. 

In  order  to  avoid  this  fault,  note  the  following  rule : 

Immediate  chromatic  alterations  of  a  tone  are  to  be  applied  in  that  voice^ 
alone  in  which  the  tone  unaltered  immediately  before  occurs. 

Notwithstanding  this  rule  answers,  in  so  great  degree,  to  all  theoretical 
principles  of  harmonic  connection  and  progression,  there  is  hardly  any 
one,  to  which  so  many  exceptions  in  the  practice  can  be  shown. 

For  this  reason,  in  the  books  of  instruction  of  later  methods,  great  sus- 
picion has  been  cast  upon  the  doctrine  of  the  cross- relation,  and  instances 
brought  forward  in  which  the  unharmonic  cross  relations  occur  in  a  per- 
fectly  natural  manner,  without  examining  the  reason  why  they  do  not  sound 
faulty. 

Some  of  them  will  be  here  adduced : 


355. 


i^p^^-^^ipipi 


^: 


Mk 


■la.*/  ''= 


W 


^^ilill^ 


MANUAL    OF   HARMONY. 


167 


) 


It  ^'         '  H  '     .J  I  I 


S 


§_^ 


^;r_  _ 


In  all  these  cases  the  cross  relation  appears,  not  formed  through  the 
simply -harmonic  leading  forward  of  the  voices,  but  either 

In  the  character  of  changing  notes  at  a^  b^  g^  or  through  contraction 
(drawing  together)  of  natural^  hut  for  the  metrical  construction,  too  cir- 
cumstantial harmonic  connections,  at  c^  cl^  €^  f^  7l, 

The  first  needs  no  proof,  and  there  is  only  the  observation  to  be  added, 
tbat  this  kind  of  cross-relations  would  probably  occur  mostly  with  smaller 
divisions  of  the  measure,  and  the  above  notation  in  half  notes  is  rare  and 
therefore  unsuitable,  because  through  it  the  simple  harmonic  foundation  ig 
expressed,  and  not  those  tonic  elements,  which  serve  for  embellishment. 

The  original  progression  of  the  voices  with  the  above  cross-relations, 
which  are  the  result  of  contraction,  is  the  following :' 


356. 


I 


d.  , 

5i 


ii 


ill 


^E^=^; 


^ 


=r- 


zis: 


Let  these  examples  be  compared  with  those  under  No.  355,  at  C^  it^ 
e,  lu 


168 


MANUAL    OF   HARMONY. 


All  these  conditions,  through  which  cross-relations  are  most  endurable 
are  wanting  in  the  following  and  similar  cases,  which  are  therefore  faulty. 


35T. 


m^^^wm. 


In  all  the  above  instances,  which  are  taken  from  practice,  but  sep- 
arated from  their  connection,  is  still  to  be  added  the  consideration  of 
the  temjio,  of  the  consistency  of  a  whole  brought  out  by  means  of  ryth- 
mical divisions,  which  will  make  all  these  formations  not  unpleasant,  but 
rather,  precise. 

Among  the  cross-relations  is  reckoned  also  a  progression  which  is  known 
under  the  name  Tritonus,  and  the  explanation  of  which  follows  here  : 

Of  the  Tritomis, 

The  tritonus  is  contained  in  the  diatonic  major  scale,  and  embraces  the 
distance  from  the  fourth  to  the  seventh  degree  (in  the  C  major  scale  the 
augmented  fourth  FjtJB.) 

This  step  from  F  to  B  embraces  three  whole  tone-steps ^  whence  its  name 
is  derived : 


35S. 


V — gy— #— «- 


-o  — 


It  is  held  to  be  unmelodic  and  unvocal  because  each  of  its  tones  requires 
an  especial  progression,  which  tones  properly  appear  assigned  to  two  dif- 
ferent voices : 


359. 


of  which  the  one  must  remain  disregarded  in  its  progression,  if  the  step 
is  transferred  to  one  voice  : 

360.  ll^l^E^^jH  ,  _ 
unless  the  melodic  succession  be  formed  thus : 


»«»•  §^^^'^^11 


MANUAL    OF   HARMONY. 


IGO 


That  this,  however,  is  not  the  only  reason  of  the  unpleasant  effect  of 
this  interval-step,  is  shown  by  the  very  often  used  inversion  of  the  same, 
which  would  likewise  require  a  two  voiced  progression. 


363. 


f^l^llE 


^F=c 


':     and  is  just  as  intelligible  and  easy  of  performance,  as  the  tritonus  appears 
difficult  and  refractory. 

Remark. — It  may  still  be  remarked,  in  this  connection,  that  the  tritonus  depends  upon 
the  diminished  triad  and  its  progression,  as  becomes  plain  from  Example  No.  362  alx)ve. 
(See  page  38). 

That  this  step  was  formerly  especially  held  up  as  faulty,  lay  in  the 
circumstance,  that,  in  connection  with  the  otherwise  customary  simple 
harmonic  formation  of  tone-compositions,  it  formed  the  only  augmented 
progression  which  diatonically  exhibited  itself.  At  this  day,  with  the 
extended  use  of  all  artistic  means,  it  is  simply  reckoned  among  the  aug- 
mented progressions,  which,  in  a  pure  harmonic  leading  of  the  voices,  are 
to  be  avoided  as  unmelodic,  or  at  least,  used  with  caution. 

The  things  to  which  reference  is  to  be  had  in  the  use  of  the  tritonus,  are 
its  situation  and  its  manner  of  appearance. 

It  can  occur,  based  either 

Upon  one  chord  (a)  or 

Upon  two  chords  (&),  e.  g. 


363.   a.                                                   h. 

nil 

if.    q    .  J±=.    fa    M^-    b       fc.^b*^     t^-d 

h"  It 

1^ — _t>a i_s — L._^ — O-i-o — L_g-d_jj — L_5ijdL L_(5-J 

5^       .t 

9'E^~i  I  -=i-  E-ri^^i^  M 

~t 

If  it  occurs  upon  one  chord,  its  entrance  is  not  unexpected,  and  the  ear 
is  prepared;  in  connection  with  two  chords,  however,  the  feeling  of  a 
forced  progression  is  easily  produced. 

Formerly  the  prohibition  of  the  tritonus  was  extended  to  the  two  major 
thirds,  which  follow  each  other  at  the  distance  of  a  whole  step,  e.  g., 

not  however : 


364. 


;^2^i^l=i^fe=^=ii=i 


tnd  it  is  not  to  be  denied,  that  this  progression  produces,  two-voiced,  the 


170 


MANUAL    OF   HARMONY. 


same  unpleasant  effect,  whereas  the  same  three  and  fonr-i  oiced,  especially 
if  it  does  not  appear  in  the  outer  voices,  is  rendered  much  milder. 


S65. 


That  formerly  the  step  from  the  fourth  to  the  seventh  degree  of  the 
minor  scale,  e.  g.^  D  to  Gr+(,  was  not  reckoned  as  tri tonus,  is  founded  upon 
the  former  usual  representation  of  the  minor  scale  itself,  and  its  harmo- 
nies.    The  effect  of  this  step,  since  it  is  augmented,  remains  the  same. 

We  return  again  to  our  Exercise  No.  353,  and  attempt  a  better  treat- 
ment. 


366. 


S66&. 


m 


& 1— (S? — 


&c. 


jiigE^p^g^i 


rJ!^i=?=:T 


1 


Exercises. 


m 


^: 


^i 


;^ 


S"^: 


4. 


fj: 


:^ 


ii; 


bO 


fI^ 


^^^felEgE 


izo- 


DjO 


l\ 


*? 


2.  Harmonic  accompaniment  to  a  given  oniddle  voice. 

This  exercise,  wliich  belongs  properly  to  the  contrapuntal  labors,  cannot 
begin  too  early.  It  is  introduced,  for  the  present,  with  the  addition  of  tho 
fundamentals. 


MANUAL    OF   HARMONY. 


Ill 


ALxa      C 


367.  t 


1^: 


Exercise, 

0  F  G  A 


D-r  G        C 


i 


In  the  treatment  of  this  exercise,  the  first  and  most  important  thing  will, 
again,  be  the  sketching  of  the  Bass.  At  the  same  time,  however,  the 
Soprano,  as  the  most  prominent  voice,  can  be  added,  e.  g. 


368. 


i-i^E: 


o — ■ 


^i^i: 


d: 


Dy     G  C 


m& 


I:E^eeIe^Ie^e^I= 


ii^i 


T 

5 

The  foregoing  can  answer  as  a  three-voiced  movement ;  through  the  addi- 
tion of  the  Tenor  it  will  assume  this  form  : 


S69. 


1^ 


—\—^ — T^^^"=^s^ — ^d— F-^ 


;i^ 


-© — 
I    I 


1^1 


§f^E£ 


-G 


— c:=i:=:^ii=izz5i=i±_^ e_Ez=i:tE 


Exercises  with  given  Alto, 


369  A. 


|16^: 


: :.-« : 


;i^i 


:5Z 


fe 


T-fi'-- 


D  Giy  0  F 


F         Bb        0 


Bb  C 


nziisz 


i^^; 


F  G  Cy  F 

4. 


F         C  D 


w. 


^^m\^=mm^m 


C  F 


p:E^: 


-» r— & 


is:  "^       ^ 


ei 


Bb 


B^  A 


172 


MANUAL    OF   HARMONY. 


wmm^\^^=^\^^^^^m 


a  D  —.J-  o  Bj?  0 

A  Tenor  voice  would  be  treated  in  like  manner. 


Exercise, 


Tenob.  C 


370. 


_(© I_fi <9 


111 


<2 c 


nszui 


Sketch  of  the  Bass  and  Soprano  : 


»T1. 


Four-voiced 


372. 


;^e=;;e£^ 


:3i 


:<s:=:. 


■»       -a 


^       *       ^       * 


^^1 


^i 


zsjn:  rs:!=z  _'«i 


SE 


ate 


•*"         -^         !^.        ~         —         -^         •*" 


:e7i:: 


S CL— 


■*—&- 


1 


373  ». 


|3=! 


Exercises  with  given  Tenor. 


E=l^l^ 


G-y       C 


-« 


^ 


G 


C         G 

: ,-C 


C  G7        c 

4. 


|3- 


125:: 


;i^^ 


jzsnz 


mi 


A  E^  A  AD  Ot!^  A  —  bO  E7  A 

These  exercises  are  to  be  continued,  until  the  sketching  of  the  Bass,  as 
well  as  the  leading  of  the  voices  in  general,  is  perfectly  pure  and  certain. 

At  the  close  of  this  chapter  it  should  be  remarked,  that  to  a  good  car- 
rying out  of  these  four-voiced  movements,  a  good  position  of  the  voices  i« 


MANUAL    OF   HARMONY, 


173 


especially  necessary ;  the  boundaries  of  the  voices  themselves  must  not 
be  overstepped,  the  distance  from  one  voice  to  the  other  must  not  be  toe 
great,  neither  must  it  be  too  small;  this,  however,  does  not  apply  to 
two  voices,  which,  for  example,  meet  upon  one  tone. 

In  this  relation  let  the  following  rule  be  noted  : 

Of  the  upper  three  voices,  the  distance  from  one  to  the  next  must  not  he 
greater  than  one  octave.  The  relation  of  the  Bass  to  the  Tenor,  however^ 
admits  of  exceptions. 

Remark. — ^To  set  the  present  exercises  in  the  Bass,  wiU  not  be  to  the  purpose,  sincQ 
they  would  appear  exactly  in  the  former  manner,  as  figured  Basses.  They  can  only 
h€  set  ioT  free  harmonic  treatment. 


CHAPTER    XVIII. 

•  Extension  of  the  Harmonic  Accompaniment, 

To  a  given  voice  in  whole  notes,  the  harmonic  accompaniment  in  half* 
notes  interchangeably  in  the  other  voices.     This  can  take  place, 
Through  two  chords. 

Through  change  of  the  situation  of  one  chord, 
Through  suspensions. 
The  exercises  will  be  marked  in  the  same  manner  as  heretofore. 


Exercise, 


Bt>G, 


373. 


m 


The  Bass  can  be  sketched  in  this  manner  : 


3T4. 


In  the  second  and  fourth  measures,  sevenths  of  secondary  chords  of  the 
seventh  show  themselves  without  preparation. 


174 


MANUAL    OF   HARMONY. 


This  kind  are  called  passing  sevenths.  They  start  from  the  fundamental 
of  the  chord,  and  always  appear  upon  the  arsis.  In  such  a  manner  they 
can  occur  in  all  voices. 

The  addition  of  the  middle  voices  to  the  above  sketch  of  a  Bass,  gives 
the  following  four-voiced  movement : 


375. 


|iii!iEi=l^= 


\ — 


tdfe^fegEElE^g 


i: 


i 


6      7 


8       7 


The  same  exercise  with  a  richer  change  of  harmony  can  be  given  in  this 
manner : 

C  FfJo^     GgJOy     AC-yb       dD        G— y  C 

376.  " 


36e?:e 


m 


377. 


Treatment : 


;i^ 


:~CL 


t--5?:^ 


'S* ?r3 -G 


I  I 


gEEEgp.^^=ifEfeife&;i 


m 


7b 


4      6 

3b 


The  next  exercise  will  exhibit  the  use  of  the  suspensions. 


378. 


F           Bb          C           D            o 

379. 


^/•(Wfmeni; 


|fc^: 


■4=H=^ 


-s--='-  ■ 


P^i 


6> g) 


9        8  6       - 


MANUAL     OF   HAUMONY, 


§il 


_(2- 


mm 


We  pass  over  the  exercises  in  the  middle  voices. 

The  using  of  the  simply  melodic  progression  in  whole  notes,  as  exercises, 
(cantus  firmus)  took  place  for  this  purpose,  viz.,  in  order  to  exhibit  the 
simple  harmonic  content  of  a  measure,  or,  as  takes  place  in  Alla-breve 
measure,  to  exhibit- it  in  its  principal  divisions  (half-notes).  If  the  exer- 
cise is  given  in  half-notes,  then  chorals  can  be  selected  for  the  purpose. 

For  personal  practice  the  fundamental  tones  of  existing  good  har- 
monic treatments  of  chorals  can  be  very  easily  drawn  off,  and  the  treatment 
attempted. 

In  the  next  exercise  the  process  will  be  be  shown. 


Choral:    0  Haupt  voll  Blut  und  Wunden. 


D7 


A     —  E     — , 


3§0. 


;^i 


1333 


'ssL 


il=ii^g^ 


GO  FbO  CF  CC 


'7b 


A         AFjfO 


1 — -^- 


-^ilj— ^:^=±-5^-ii? 


— I (9- 


.5^-L_-^ 


C     G 


^7\ 
.7  D        GO 


G-y     C  D-y    <J 


r7\ 
E 


-<9-r- 


:=>5:: 


z^ 


3Eb=d=ElE==[| 


The  treatment  of  this  choral  can,  according  to  the  above  exercise,  be 
t.he  f  blowing : 


3§:/ 


176 


MANUAL    OF   HARMONY. 


rs\ 


i=7^1zf:r:±t=5;:=:i=-=::«-L-e=--p-f_-:5=.Taiz±rs=::f= 

iff      ',    s    I     ',  '>     '    '      '    'i 

I  I  I  J  J     <=(  t       I  I       i 


'^mw^^mM^mmi 


^^^^B: 


I  'l 


—-fg— 


i/— ,e- 


-J: 


^j  i 


r— r 
I 


■F 


^£^I^E^I 


II  1  I  u   I  I  u 


^"^Ie^^I^ 


After  sufficient  practice  and  certainty  in  the  management  of  tlie  simple 
harmony,  we  can  proceed  to  a  farther  development  of  the  leading  of  the 
voices,  by  means  of  the  passing  and  changing  notes. 

For  this  purpose  will  follow  in  the  next  chapter  the  farther  discussion  of 
melody  and  melodic  progression. 


CHAPTER    XIX. 

On  the  JDevelopnient  of  Melody/, 

"We  are  not  to  treat  bore  of  the  invention  of  a  melody,  but  of  its  devel- 
opment, and,  what  is  most  important  for  our  harmonic  exercises,  to  treat 
of  it  in  order  to  learn,  by  the  elaboration  and  farfhioning  of  melodies,  to 
know  and  use  what  in  them  is  essentially  harmonic. 

AH  will  here  depend  upon  the  recognition  and  comprehension  of  the 
following  principles : 


MANUAL     OF    HARMONY. 


17. 


Every  melody^  however  extended  and  developed  it  may  be,  has  a  founda 
iio7ijust  as  simple  as  those  ive  have  used,  as  exercises,  in  our  last  examples. 

Every  harmonic  leading  of  the  voices,  however  complicated,  admits t 
therefore,  of  reduction  to  a  simple  connection  of  harmony. 

In  order  to  recognize  this,  it  is  necessary  to  learn  to  distinguish  the 
essential  notes  from  the  subordinate  and  accessory  work. 

We  select  to  this  end  the  analytic  method,  and  endeavor  to  develop  the 
following  melody,  which  we  will  write  down  in  the  simplest  manner 
according  to  the  above  mode  with  indication  of  the  fundamental  tones. 


-         Bj         F 


c^ 


F         ~ 


:^^:2eI= 


-dZi 


mm 


M\ 


Both  melody  and  harmony  are,  as  selected,  simple,  and  the  latter  may 
be  carried  out,  four-voiced,  in  the  following  manner  : 


3§3. 


i^i^i 


g^ajjjg 


r- 


iiiiiiia: 


=;rJ <9 


'r  \t  *  %■  T  «jr 


i 


liililll^B 


X>         6,.^^   Xrr^      --^ 


•  Before  we  proceed  to  a  farther  development  of  this  movement,  it  becomes 
necesary  to  premise  what  is  to  be  mentioned  concerning  the  rythmical  for- 
mation of  a  melody. 

A  melody  can  be  either  a  musical  movement  without  definite  boundary, 
containing  more  or  less  measures,  as  it  is  often  found  as  theme  (motive  of  a 
composition),  or  it  can  be  a  whole,  separated  and  bounded  by  means  of 
Antitheses. 

In  the  last  case  it  is  called  a  Period,  and  it  contains  then,  as  a  rule 
eight  measures,  which,  in  two  divisions,  each  of  four  measures,  form 
antitheses.  These  antitheses  or  divisions  are  often  called  "  thesis  and  anti 
thesis"  (Vordersatz  und  Nachsatz)/ 


178 


MANUAL    OF    HARMONY. 


■  The  more  complete  treatment  of  this  subject  belongs  to  the  doctrine  of 
Form.* 

That  the  above  movement  will  form  a  period,  is  seen  in  the  close 
of  the  whole,  and  it  will  be  necessary,  above  all,  to  seek  out  the  separating 
point  of  the  divisions. 

This  point  of  separation  is  very  often  discovered  in  the  cadences,  whicli 
either  as  imperfect  whole  or  as  half-cadences,  show  themselves  as  plagal  in 
the  middle  of  the  movement. 

Such  a  half-cadence  (in  general,  a  close  in  the  dominant)  is  found  in  our 
exercise  in  the  sixth  and  seventh  measures,  and  the  separating  point  of 
the  divisions  of  the  periods  may  be  assumed  to  be  at  the  place  where  the 
sign  t  stands. 

The  first  division,  the  thesis,  would  accordingly  receive  seven,  the 
antithesis  six  measures,  each  of  which  can  be  rythmically  altered  so  as  to 
contain  four  measures.     This  may  take  place  in  the  following  manner  : 


3S4. 


If  we  add  the  harmonic  accompaniment  selected  above,  we  obtain  a  com 
plete  musical  period. 

It  needs,  also,  only  a  glance,  to  enable  us  to  see  that  all  farthei 
transformations  into  various  kinds  of  measure,  e.  ^.,  into  4y  9  >  o  or  ^ 
measure,  admit  of  easy  accomplishment,  e.  g. 


3§5. 


pr%=f^:E^ 


EEE^ 


-6(-i- 


I^ 


M¥^l 


&|H'"nE^ESE?E|E^EE?E 


3^ 


^E^^^  "^^^^^m. 


&c. 


•fcc. 


.  We  proceed  now  to  the  tonic , variations  of  the  melody,  and  add  to  it 
•passing  and  changing  notes,  e.  g. 


^86. 


Spjtm^JM^ 


*  See  the  work  of  this  author — "  Die  Grundzuge  der  musik  xlnchen  Formeny — (Leipsi<^ 
<G.  Wigand.) 


MANUAL    OF    HARMONY. 


4^9 


^ii^li^m^^ii^ 


Still  richer  use  of  all  by- tones  could  give  the  following  formation  : 
Adagio. 


3§7. 


I^^^IP^^^^E*^^^! 


.e-^j 


Originally . 


5^-'tf*= 


^^^^^W^0^^^m^\ 


?r-=3: 


X=t- 


m 


^* 


liH^Efei^lill^illii 


--iS' 


The  simple  melodic  progression  found  below,  will  be  easily  recognized  as 
the  fundamental  Toice.  That,  however,  the  above  melody  is  carried  out 
with  reference  to  the  original  harmony,  will  immediately  become  evident, 
if  we  add  the  other  voices  with  the  few  deviations  conditioned  by  the  upper 


voice : 


38§. 


Adagio. 


f  I 


1     J      I 

-0-  ■*-  -0- 


See; 


i=f#=^ 


^^^^=fe^^^=I^^^EEl| 


180 


MANUAL    OF   HARMONY. 


I  r   I 

♦ J k*—. 


■■^-F- 


wmm 


We  may  remark  concerning  the  octave  parallels  in  the  middle  voices, 
to  be  found  in  the  third  measure  of  this  example,  that  they  are  to  be 
regarded  as  faultless  if  they  do  not  occur  singly,  but  appear  only  as  a 
means  of  additional  strength,  in  a  more  extended  succession,  for  the  inten- 
sification of  a  harmonic  and  melodic  progression.  The  movement  is,  in  this 
case,  to  be  regarded  as  three-voiced. 

As  little  independent  worth  as  this  example  has,  it  still  served,  here,  to 
show  of  what  development  the  simplest  melodic  and  harmonic  movement  is 
capable. 

The  advantage  of  the  contemplation  and  recognition  of  these  melodic 
and  harmonic  relations  is  too  great  to  allow  us  to  forbear  to  furnish  another 
example  in  the  following  interesting  movement. 

The  fundamental  harmonic  progression  is  just  as  simple  as  that  shown 
before.  v  , 


389. 


^ssiiig^m 


<9- 

-O- 


m^Mmmm 


m^; 


'^\m^ 


w- 


igyii^^i^^ie 


This  movement  forms  a  period ;  the  middle  close  is  easily  found  in  the 
half-cadence  of  the  seventh  measure. 

We  omit  here  the  various  kinds  of  measure,  and  select  the  following 
division : 


300. 


r  ir  u  I    T   1    1     ^  w^  I 


,    ^  .   .      ...         t^  . 


MANUAL    OF   HARMONY, 


181 


I         The  development  of  the  upper  voice  may  take  place  in  the  following 
^1     manner,  reference  being  had  to  the  harmonic  progression  : 


'^'-  W^^^^^^^^^^^ 


What  part  the  other  voices  can  take  in  melodic  development,  the  follow- 
ing movement  from  the  Ej?  major  quartette  of  Beethoven  will  show: 


Viola. 


ViOtOXCKLLO. 


1 3#iiE3Efe^E^.^^^ 


-w—^-z '— ^ 


^-l 


^^^^^^^E^^^^ 


_j£:^*:      t.  ^t.      ♦•    .^T^  _      ^ 


i^^: 


3EiMi^^!lS=eii 


fe§=i3^-pj^^ifeii 


-^- 


A  comparison  with  No.  390  will  show  the  melodic  and  harmonic 
variations. 

There  now  follows  still  another  alteration  of  the  original  melody,  out  of 
the  same  composition : 


182 


MANUAL    OF   HARMONY. 


S93. 


_L,<_0 ^ y^^_#_^ F-#-* h— ^ 1 i 1 1 1 1 *-+-# #• 


trF=;*: 


1^ 


The  other  voices  show  themselves  in  the  following  alteration : 
394.  ^  ^ ^ 


^-^p 


^^^  ^  1^^  ^^  — ^  &c. 


These  hints  in  reference  to  melodic  development  may,  here,  suffice,  and 
be  left  to  personal  practice  or  special  guidance. 

Remark. — ^The  mechanical  element  in  the  whole  proceeding  should  not  occasion  mis- 
take ;  for  just  so  certain  as  it  is  that  in  composition  one  does  not  always  proceed  in 
the  way  shown  above  (even  if  Beethoven,  in  the  later  alterations  of  these  original 
melodies,  could  not,  sometimes,  proceed  jotherwise),  in  even  so  great  a  degree  was  it  here 
our  only  object,  partly,  to  set  in  the  right  light  the  relation  of  our  previous  exercises  to 
the  practical  side,  and  partly,  to  gain  a  clear  insight  into  complicated  compositions  them- 
selves. 

As  concerns  the  accompanying  voices,  they  arose  of  themselves  out 
of  the  simple  manner  of  harmonizing,  required  little  alteration,  and 
showed  themselves,  even  if  subordinate,  still  not  on  that  account  insig- 
nificant. 

It  yet  remains  to  speak  concerning  other  kinds  of  accompaniment,  which 
will  be  done  in  the  next  chapter. 


UA.SVAL     OF   HARMONY.  188 


CHAPTER  XX. 

On  Development  of  the  Accompanying  Voices, 

The  last  examples  of  the  foregoing  chapter  Lave  already  shown  in  what 
manner  the  accompanying  voices  take  part  in  harmonic,  metrical  and 
melodic  development. 

There  are,  however,  still  other  kinds  of  accompaniment,  which  are  known 
under  the  name  of 

THE    FIGURATED    ACCOMPANIMENT. 

This  is  not  adapted  to  the  character  of  the  vocal  parts,  and  may  be  used  for 
them  only  in  a  very  limited  manner.  In  the  following  investigation, 
instrumental  music  only  will  be  treated  of. 

By  figurated  accompaniment  is  understood  the  kind  of  accompaniment 
arising  through  metrically  uniform  transformation  of  the  simple  chord- 
tones,  e.  g. 

Simple  harmony  :  Figurated  accompanimeni  : 

a. 

•^  ^  fLlJ--     [ZIj  fij     ' Ji-     ^^     "^^ 


VJ 


— 0-0-0-0- G — f — 0  0-0-0-^-0-^ -0-1 -ip — Li — ^'-•— i r- — *-^  • 1 

■   '«L-'>         4J^   >   ^  '^^   ^^^   ^^ 


ffe -^~0-^  -0 f-*-«-*-i 

I     j     I       1.1^     j     I  k.^     &c. 

The  accompaniment  at  ci  is  harmonically  figurated.  The  figures  arising 
therefrom  are  called  also  broken  chords.  That  at  b  is  metrically  figurated^ 
and  that  at  c  is  melodically  figurated.  The  figures  which  have  arisen 
from  the  last  are  formed  from  changing  and  passing  notes. 

Any  accompanying  voice  can  be  used  for  such  figuration,  either  alone  or 
IQ  connection  with  other  voices. 

We  select  the  beginning  of  Example  No.  382,  in  order  to  attempt  some 
kinds  of  accompaniment. 

i^        This  may  be  preceded  by  the  following  remarks : 
f'        If  the  figures  repeat  themselves  uniformly  {e.  g.  in  broken  cliords),  then 
I 


184 


MANUAL    OF   HAR3fONT, 


all  the  rules  of  the  harmonic  leading  of  the  voices  are  to  be  observed  at 
the  CHANGE  OF  THE  CHORDS,  as  ivell  as  in  the  reduplication. 
"We  must  not  write : 


396. 


'^^^m^^0^ 


9— a 


-J^ 


m 


■-f^^-- 


~^r. 


but  somewhat  in  this  manner  : 


-^ _,_«_,.  _•, — __# — 


307.    { 


"  ^:^™i, — j^'^^A— i — 1 y-* —0-1 — '■■ — f  — -^-#-1 #-j — #-- FF 


At  the  change  of  the  harmony,  the  last  note  of  one  figure  and  the  first 
note  of  the  next  must  not  form  a  false  progression  with  any  other  voice,  e.  g. 

not:  ietUr :  twt: 


«0§.    ' 


im 


i^i^^fi 


"^     -rr 


not  letter: 


^^^m^ 


,=%. 


1 


The  harmonic  figuration  also  affords  the  means  for  forming  one-voiced 
movements  in  greater  perfection.     The  examples  will  begin  with  this  : 

309.  One  iwiced : 


MANUAL    OF   HARMONY. 


185 


That  these  movements  are  calculated  for  an  instrument,  probably  such 
as  a  violin  or  clarionet,  is  easy  to  be  seen. 

400.  Two  voiced ': 


m 


:t:zz:=it±it:: 


1-: 


^iizzziiz: 


'M 


Tliree  voiced: 
in  the  niicldla  voices: 


in  the  lower  voice: 


ife 


M^m^^ 


3  ^3  3 


d": 


in  the  upper  voice: 

-9 •-H 


In  two  voices: 


T^t.—-=X, 


i 


ip|E&=^^^E^^^ 


The  figuration  in  the  four-voiced  movement,  after  these  attempts  witl 
the  above  example,  will  be  equally  easy  of  acoomplishmer  t. 


Oty^r^rM^^  -^^r^fCP^y-^-^  - 


186 


MANUAL    OF   HARMONY. 


Instead  of  this  we  prefer  to  select,  as  an  example  of  manifold  figuration, 
the  following  passage  from  the  above  quoted  quartette  movement  of 
Beethoven. 


101. 


±^=:^ 


:^=3 


9—^- 


:q-— . 


fc^^::£:i^i::&i:£i=T=tj£,,jfe._f_-^^^f^ 


;b: 


ptzz. 


m^^ 


l=^E^^E$=\^-^^^^-E$E^=i 


* 


fci^ 


* — i- 


i=:|: 


'■w^ 


feE 


-<<— I— «!— I 1— J- 


9Ji^ 


*• 


Slr=g^i=fei^?^^^Ef=^=fe^=lE:| 


liEE=S^.^=2^^-=lEf=^=^,%.i^,^I=§ 


I 


MANUAL     OF    HARMONY. 


187 


#— ^ 


in 


il6l^?=^^=i=i=s^EElE5=^=!^_^i^i 


This  whole  rich  development  rests  upon  the  foundation  given  in  Nos. 
390,  391  and  392,  and  wherever  the  harmonic  change  enters,  the  leading  of 
the  voices  is  carefully  observed. 

If  we  wish  to  obtain  a  clear  insight  into  such  elaborated  compositions,  and 
arrive  at  an  understanding  of  their  inner  harmonic  structure,  it  will  be 
very  useful  to  reduce  compositions  of  this  kind  back  to  their  simple 
foundation ;  industry  in  this  will  reward  itself  by  enrichment  of  knowl- 
edge of  many  kinds,  and  by  our  being  rendered  capable  of  formations 
of  our  own. 


CHAPTER  XXI. 

Tlie  Exercised  in  the  Three-voiced  3Iovenient, 

With  few  exceptions,  the  four-voiced  form  of  writing  has  been  used  for 
our  exercises  hitherto,  and  although  it  affords  greater  completeness,  and 
appears  most  adapted  for  the  harmonic  connections,  the  three-voiced 
movements  are  also  of  much  advantage,  since  they  are  especially  calcu- 
lated to  make  the  leading  of  the  voices  more  skillful  and  many-sided. 

AVe  begin,  as  before,  with  the  problems  with  figured  Basses. 


8  7 


6  6 
5  4 


0 


6  2 


*•»•  i^3=^^^:^Ei^= 


d=I=: 


:rq: 
zzst 


188 


MANUAL    OF   HARMONY. 


4 
6       3 


-^ 


m^^ 


3^ 


1 


The  three-voiced  movement  is  sufficient,  indeed,  for  the  triad,  but  the 
leading  of  the  voices  will  often  result  in  the  omission  of  one  of  its  inter- 
vals ;  in  the  case  of  the  chords  of  the  seventh  one  interval  must  naturally 
always  be  wanting  ;  this,  however,  can  never  be  the  seventh  itself.  As  a 
rule,  the  fifth  can  be  omitted,  as  has  already  occurred  in  the  four-voiced  move- 
ment, and  the  fundamental  also  in  many  cases ;  the  third,  as  the  interval 
which  determines  the  mode,  can  only  be  omitted  in  a  few  cases,  without 
producing  an  especial  emptiness. 

The  treatment  of  the  exercise  is  the  following,  to  which  a  few  remarks 
will  be  added : 


p^^i^l 


¥=^ 


»Eg=|g^g^E|^g^Ep 


»-n— P G-^-&- 


pE^gE^Egr^TEl^^g^^ 


4 
6      3 


6 
6         5 


ii^^^i3^i^^i^= 


In  the  fourth  measure  is  found,  at  NB.,  the  chord  of  the  sixth  and  fourth 
of  the  diminished  triad,  E-G-B]?.  It  stands  instead  of  the  chord  of  the 
Becond,  Bb-C-E-G,  of  which  the  fundamental  C  is  here  omitted.  For  four- 
voices,  this  place  would  stand  thus : 


MANUAL    OF   HARMONY. 


180 


404. 


Concerning  this  chord,  compare  what  is  mentioned  page  155. 

In  the  fifth  measure  a  fourth  represents  the  chord.  Now,  although  a 
fourth  can  neither  in  the  three-voiced  nor  in  the  two-voiced  movement, 
have  the  worth  of  a  complete  chord,  as  can  the  third  and  sixth,  yet, 
in  cases  where  the  chord  of  the  sixth  and  fourth  as  passing  chord  can 
be  used  upon  the  arsis  in  the  four-voiced  movement,  probably  the  sixth 
or  third  of  the  fundamental  chord  can  (for  the  sake  of  a  better  lead- 
ing of  the  voices)  be  omitted  in  the  three-voiced,  so  that  the  fourth  alone 
remains,  marking,  here,  fundamental  and  fifth  of  the  original  chord. 

In  the  two-voiced  movement,  the  fourth  will  occasionally  take  the 
place  of  the  chord  of  the  second,  especially  in  the  case  of  the  passing 
seventh,  e.  g. 


I       I 


405. 


Four-voiced,  the  above  place  in  Example  No.  403  would,  complete,  stand 
thus: 


I— ^- 


406. 


IS fi)_I-lJ5l ^ IC 


In  the  eighth  measure  of  Example  No.  403,  the  chord  of  the  sixth, 
fourth  and  third  is,  by  the  skip  of  the  Alto,  formed  complete. 

The  tenth  measure  exhibits  apparently  a  chord  of  the  sixth  and  fifth. 
Fundamentally,  the  fifth  here  is  nothing  else  than  the  suspension  of  the 
fourth,  which  here,  however,  through  the  progression  of  the  Bass,  becomes 
a  third.     Four-voiced  this  becomes  plainer : 


190 


407. 


MANUAL    OF    HARMONY, 

9-     -r-         ^      •*•  — 


'  r 


iiiEEEiE^I 


-^---.- 


:1=d=I=: 


'zst=:^ 


;P3= 


I 


The  closing  measure  of  Example  No.  403  shows,  through  the  octave  F, 
that  the  triad  can  appear,  in  such  cases,  even  without  third  and  fifth. 

That  the  omission  of  the  third  is  often  conditioned  by  the  leading 
of  the  voices,  is  shown  by  the  first  and  second  measures  of  the  next 
example. 


i08. 


|igzzzp:zz£i^zgz=g^.£^; 


m^^^^^^^^^^^: 


6  7 

4       «      - 


3      65 


^fr>-3— ^— 1—74 


:pt 


&^ 


fJN: 


^^li^^il 


5  - 
4  3 


^  7     6 

3     6    6      4    -    $ 


gfil^EE 


rzq: 


;iii: 


The  omission  of  the  third  takes  place  best  upon  the  arsis,  as  here  in  the 
last  measural- division ;  upon  the  thesis,  (accordingly  at  the  beginning  of 
the  measure),  the  third  should  not  be  wanting. 

Farther  exercises  are  to  be  left  to  the  especial  guidance  [of  the  teacher]. 


Exercises  in  the  Three-voiced  Movement  to  a  given  Upper 

Voice, 

The  following  exercise,  with  indication  of  the  fundamental  tones,  is  to 
be  worked  out  three-voiced  : 


■  *o».pe; 


MANUAL    OF    HARMONY 

C  G  C  —  F  AD 


101 


c 


\mm=m 


Treatment. 


r 


410. 


sj^ii^i^i: 


'\{ 


r—G—^—G 


^^Mmm^^mm^mi 


i^^fMiiii^i-^ilii 


izTs: 


^\ 


tcithout 
fundameiititl. 

This  treatment  needs  no  explanation. 

The  choice  of  the  middle  and  lower  voices  will  depend  upon  the  position 
of  the  chords  in  general.  Thus,  in  a  low  position,  the  Tenor  as  middle 
voice,  will  be  more  suitable  than  the  Alto,  just  so  the  Tenor  can  be  selected 
as  lower  voice  instead  of  the  Bass. 

For  the  following  example  the  Tenor  is  selected  as  middle  voice,  since 
its  movement  attaches  itself  more  to  the  Bass,  while  on  the  other  hand, 
the  simple  song  of  the  Soprano  appears,  of  itself,  isolated. 

The  previous  Exercise  in  more  extended  harmonic  treatment ; 


,411.  p^! 


E  A 


G  C 


D  GJfO.^ 


1)  D         G 

— S> — T 


^1=1 


413. 


T/'eatMcni: 


IF 


^. 


mmEmmmm 


s 


iSHgll 


6 


G 


9^^Bil|gg|Bggp6g£i^; 


KB. 


In  the  fifth  measure  at  NB.  appears  the  real  ninth-suspension  (through 
the  position  of  the  voices),  as  second,  which  occurs  very  seldom,  and  only 
between  Tenor  and  Bass.  In  this  connection  it  is  to  be  remarked,  that  a 
second-suspension  cannot  exist,  because  the  second  depends  upon  the  inver- 
sion of  the  seventh,  and  governs  itself  according  to  the  progression  of  tho 
latter,  e.  g. 


192 


3fANUAL    OF   HARMONY. 


Inversion 


-&^*-^g- 


413. 


-■ f^^<m^a — ■ — v^ L 


I     I 


r 


i 


Exercise  in  a  middle  voice. 

Tenor.       d         A         Bjj        C         g  eO        i> 


^^ 


A  D 


4H.  gH^g^l^ 


-©—  - 


i^ie^ff 


As  upper  voice,  the  selection  of  the  Alto  is  here  most  to  the  purpose. 


415. 


^T3=F 


ee: 


i^lilSlll 


!!S-=S=:l^iE=iE}lBES=ll: 


3     6 


ii^i^l^j^l^^^l-^^H^feME 


The  same  Exercise  with  the  following  determination  of  chords 

D  o       A— ^  Bb  Q-      C  F     Bb  Co-    »       Bb  F      o  rO      »  A 


416  gJ£gEgpjg|g|;|gE|?i;E|^|=:|g^E|^;||^p| 


7)'eatment: 


417. 


-T— (2J-!S> 


(2 


|BlEilg^i|=^tE|EgElEgg|^gg^"5| 


?!iiiHliiH^"lFJ 


::-siizzz::— 


7 

«    - 


©jFEEE:i=i 


:|_^g. 


G  G 

4 


=^ 


3- 


=.3^E^I 


|J|^^|EE=| 


P-T— «- 


?:=^ 


;E^iEt=E 


iiii[E^: 


13] 


^ii^ll^i^ii; 


6      4  6       7 


6         «      6 


i^^i-^^^i^lPi^^^^lf 


MANUAL    OF   HA  HMO  NY. 


m 


The  next  to  the  last  measure  affords  the  proof,  that  even  the  sixth  can 
be  suspension. 

For  farther  practice,  former  exercises,  which  were  given  for  the  four- 
voiced  movement,  may  be  used. 


CHAPTER  XXII. 

On  the  Ttvo-voiced  Movement, 

The  great  meagreness  of  the  two-voiced  movement,  in  a  purely  harmonic 
)oint  of  view,  allows  it  rarely  to  appear  adapted  for  other  than  contra- 
rantal  labors,  in  which  it  first  receives  actual  significance  and  comqs  to  be 
applied  even  in  polyphonic  movements,  e.  g.,  in  fugues. 

If,  indeed,  for  simply  harmonic  use,  the  metrically  and  rhythmically 
various  formation  of  the  voices  makes  the  two-voiced  movement  toler- 
able, still  the  contrapuntal  development  of  two  voices  can  alone  free  them 
from  the  monotony  of  many  successions  of  thirds  and  sixths,  and  give  this 
movement  that  individual  completeness,  which  every  other  polyphcraic  move- 
ment must  possess. 

The  omission  of  one  or  more  intervals  will,  In  every  case,  necessarily  take 
place  in  connection  witli  this  movement.  With  the  triads,  it  will'  generally 
be  the  fifth  or  the  fundamental.  If  chords  of  the  seventh  are  to  be  applied^, 
then,  of  course,  the  seventh  cannot  be  omitted.  Octaves  and  fifths  are  seldsDm 
to  be  introduced,  since  they  appear  too  empty ;  the  fourth  could  ©oly  be 
admitted  in  a  few  cases  where  the  chord  of  the  sixth  and  fourth  can 
regularly  stand,  or  if  it  occurs  instead  of  the  chord  of  the  second.  (See 
page  188). 


Example: 

418 


bO 


p 


^nii^^^: 


F 


Ilia: 


;[f 


419. 


Treatment : 


A  ^ 


^ 


^i 


mf^mmm^ 


m: 


5        3  6 

7a: 


6  3  6  6  3 


3  1 


I^l^l^ 


i 


194 


MANUAL    OF   HARMONY. 


The  omission  of  intervals  is  plain  through  a  comparison  of  the  fun- 
damental tones  of  Example  No.  418.  Want  of  clearness  of  the  harmony 
•will  be  rare  in  connection  with  this,  since  each  chord  explains  itself  through 
its  situation,  i.  e.,  through  the  preceding  and  following  harmony. 

The  same  exercise  with  the  following  marking  : 


F— . 


4*0.  p^; 


;i^i; 


G 


^--fi- 


m^ 


421. 


Treatments 


/  —is>—^ 

— ©- 

■   "O 

-        1 

■ 

T 

2 

6 

— t 

. 

6         ^ 

5 

^2 

— 

s 

-a—  ■ 

V5115=:p'-[:=: 

;-t=E- 

-X 

=E-: 

-=^ 

^ 

— o- 

-5-j 

— ©- 

w- 


— ©- 


i 


4     - 
3     - 


6 


w^mmmmmm 


Most  of  the  exercises  exhibited  in  the  third  part  trespass  upon  the 
domain  of  counterpoint.  The  difference  consists  only  in  this,  viz. ;  that  here, 
the  succession  of  the  chords  is  prescribed,  and  it  only  remains  to  form  the 
leading  of  the  voices,  while  in  the  contrapuntal  exercises  the  knowledge  of 
harmony,  as  well  as  certainty  in  its  use,  is  assumed,  so  that  the  suc- 
cession of  the  harmonies  can  be  left  to  our  own  choice. 

We  may,  therefore,  regard  these  labors  as  a  useful  preparatory  exercise 
for  those,  as  they  also  afford  at  the  same  time  an  insight  into  the  relation 
of  harmony  to  counterpoint. 

The  exercises  in  the  next  chapter  are  also  to  be  considered  in  this  light, 
since  they  drop  the  above  limitation  of  a  prescribed  succession  of  chords. 


MANUAL    OF   HARMONY. 


m 


CHAPTER    XXIII. 

Harmonic  Elaboration  of  a  given   Voice  in  Melodic  Develoj)- 

tnent. 


By  melodic  development  of  a  voice  is  not  here  to  be  understood  that 
richer  ornamentation,  such  as  Chapter  XIX.  exhibited.  Through  met- 
rical variety  of  their  measural-divisions  alone  the  simple,  choral-like  pro- 
gression of  oui*  earlier  exercises  will  be  avoided,  and  thereby  opportunity  be 
given  to  learn  to  develop  better  the  voices  of  the  harmonic  accompani- 
ment also. 

The  following  exercise  will  make  this  plainer  : 


422. 


_e_._iz 


¥^ 


^ — 


.(2-      f2— S(- 


r^^9,T-^~.- 


|gE.^E|^EEEf^EEE£|-z^-E|-:EE-|^ 


The  choice  of  the  chord- succession  is  left  to  the  treatment  itself. 

Even  if  the  kind  of  measure  selected  will,  of  itself,  produce  a  like 
melodic  leading  of  the  voices  to  be  elaborated,  still  especial  attention  must 
be  given  to  a  good  leading  of  them,  according  to  the  principles  developed 
in  the  previous  chapters,  if  a  free,  skillful  treatment  of  them  is  to  be 
attained. 

This  exercise  will  follow,  first  in  three-voiced  treatment. 


423. 


zzc: 


-^ 


::zgsi 


It 


TV-      ^9- 


E^ 


_fi-*:o. 


P^^ 


^ 


-f=i^ 


i^HUill 


-=e: 


9  8 


7  6 


7  6 


6       G 
7  6   4       5 


i 


This  treatment,  after  what  has  been  remarked  in  connection  with  the 
three-voiced  movement,  needs  no  farther  explanation. 

The  harmonic  treatment  of  this  melody  as  middle  voice  will  show  its 
many-sidedness,  and  may  be  recommended  as  a  useful  exercise. 

In  order  to  be  able  to  retain  the  Alto  voice,  we  transpose  the  melody,  foi 
the  sake  of  the  better  position,  to  F  major. 


196 


■  MANUAL    OF    EARMONY. 


424. 


mm-^mm^mm^m 


cantus  Jlrmitt. 


iilE^I-^EE: 


■^'1^^4^1"^E|ii[^ 


iillElliii 


7      683984      5 


9  8  7 


-F 


gE^lllgi^i 


The  explanation  of  the  chord  of  the  sixth  and  fourth  which  enters  free 
in  the  fourth  measure,  is  found  in  what  was  remarked  in  Chapter 
XV.  concerning  the  passing  chords.  It  arose  accidentally,  through  the 
progression  of  the  Bass  by  degrees,  and  stands,  here,  in  the  place  of  the 
chord  of  the  second. 

The  treatment  of  the  same  cantus firmus  transferred  to  the  Bass: 

425. 


Lfi^gl^^^l^i 


¥■ 


?G (S. 


•»  • 


mfm^^i=^i^=^mi 


.(2-«_ 


e 


c./. 


K 


-^-©-.— 


4  ^      5    - 

6j8r  6     36     3b2-4     5-G 

■ ■  ' '  VS^^^ 


»-  -  & — ^ — H'-rH' — » — 1-^ H- — &-( — jKTv — r^  .   r 


This  treatment  exhibits  a  weakness  in  the  third  and  fourth  measures,  in 
the  harmonizing  of  the  sustained  A  of  the  Bass.  In  like  manner  the  bare 
fourth  in  the  sixth  measure  is  a  very  imperfect  representative  of  a  chord, 
unless  we  wish  to  explain  it  as  a  passing  note. 

If  we  wish  to  develop  the  leading  of  the  voices  still  farther,  we  can 
mtroduce  passing  and  changing  notes  interchangeably,  into  the  two  voices 
to  be  added,  e.  g, 

cf.  ., — .  ^ — - 


15 


426. 


^ : 


S^Ef^E 


l!S= 


-#-•- 


E 


7J91 


EEgB-r-r-T±± 


pitztzp^F 


0       7      6 


t^KEHE^i 


==E^F=E 


MANUAL     OF   HARMONY, 


U 


e; 


19; 


m 


ig3_^^t^f=rf=^-:z4^: 


EE|^E3_^-c 


if^ 


6 

5  3 


3     7 


i!=3E^^EiEg^ricE»E_E: 


Of  the  remaining  treatments,  that  of  the  cantus  Jirmus  in  the  middle 
voices  will  here  be  given  : 


427. 


£ 


S^Egg 


#-==u-#-, 


c./. 


HIe^^^"^ 


llElil^il^m: 


6  7 


6  9       6       G 


S^^iti^. 


^-# 


^E?EHEEEEEEt'~^" 


f3= 
Si 


0-^-0-^. 


li^^^iysii^iE 


■^  ^        ^ 


:E=t^^ 


-r— S" T- 


J^-il 


9  8 


6 

5  ^  m  m 


gl^^gEgEE^lEEEEEEEp^ 


5  6 


i=3=iE«E 


I^IE 


As  examples  of  four- voiced  treatment,  the  following  may  stand  here : 

4  2  S  •   Given  toice :  ,_ .^ 


JsStE 


{^HsBg^gg^gggg^ 


198 


MANUAL    OF   HABMONY. 


439.    Four-voiced  treatment  : 

c.f.  .     . 


^^Em^^^^^^mmw^m^ 


^  "^  ^   a    ^ 


^m^m^^k 


m^^ 


4  3 


9     8  6  6     6-6 

7     6     7_4    3    51]  543     867 


za- 


SES?E^ff?E?£jE 


I 


In  the  fifth  measure,  at  NB.,  the  skip  of  the  Tenor  into  the  seventh  ia 
not  good,  because  the  Soprano,  at  the  same  time,  makes  a  long  skip  in  the 
same  direction,  into  the  fundamental  G ;  only  the  position  of  the  Alto  can 
excuse  this  case. 

In  the  same  measure  is  found  the  chord  of  the  sixth  and  fourth  of  the 
augmented  triad,  the  original  fifth  of  which  is  prepared  (pages  91  and  92). 
It  stands  here  in  the  character  of  a  suspension  from  below.  (See  Suspen- 
sions, Chap.  XII.,  page  116). 

The  same  cantus  firmus  in  the  Alto,  transposed  to  D  major  : 


430. 


-& — ^- 


c./. 


isipj 


-.« — ^ 


£EEc"£EE 


NB. 
:iCi fi, — ,o_. 


^_0- 


X- 


3EEEEaEEF£5 


;i 


i*l^ 


5      — 
4      3 


■H 


:i~?' 


.X ^ 


?  i 

^ 4      7 

~Q~,vzzzz: 


I0~== 


MANUAL    OF   HARMONY, 


199 


^       tt    ^    ^ 


— -H— -r— (2- 


NB. 


-f^- 


Q-r-n- 


11^111== 


7      6      6  3      6      7 


iLipr^-^ 


iZTis: 


In  the  fourth  measure  are  found  suspensions  in  three  voices  (see  page 
117).  In  the  fifth  and  sixth  measures  the  position  of  the  Alto  and  Tenor 
5  is  not  good,  because  the  distance  from  one  to  the  other  is  more  than  ait 
octave. 

Of  the  remaining  treatments,  that  of  the  canius  Jirmus  in  the  Bass  will 
here  follow : 


4S1. 


Si: 
I* 


E 


^TE^^j 


-G-f-o — ?5-T-S'-T— ri 


-(5L«_^_(2. 


=iz^°—Y—^-^k^-¥(^'^-^--^-'- 


^l^l^l^ggl 


=f-^ 


^=&=^^- 


iig^iiiif 


^sSPii 


e./      4  3  6 


6 

4 

6  _2  6  3 


6^356  6      6       4 
5^     ^t^-     4  6  3    


NB. 


The  introduction  of  the  chord  of  the  seventh  of  the  seventh  degree,  in 
the  fourth  measure,  is  not  clear,  because  the  fundamental  lies  imm©- 
liately  above  the  seventh.     (See  page  69). 

Besides  this,  its  progression  does  not  ensue  here  according  to  the  leading 
of  the  leading  tone,  but  in  the  same  cadenciug  manner  as  with  the  other 
chords  of  the  seventh  :  Cj{  "7  Fjf.     (See  pages  68  and  69). 

The  treatments  of  this  canius  firmus  with  a  leading  of  the  voices  in 
which  there  is  more  movement,  can  be  carried  out  in  this  manner : 


200 


MANUAL    OF   HARMONY. 


II,       *i ^  •, 


432. 


O T-® / 


t 5>- 


E3; 


1 


B-^il==r=*' 


i-#-«-#- 


^r^iSii^; 


,^^^^:^ 


:3:zFt: 


G 

4       5 


F*= 


iill^g^^iN^iEi=sii^p 


•^ 


w- 


;l^5E^^EE:E=ii 


i-«--^E^_^i^ 


i 


fclf^gi^li^^E^llli?^gE|^iEi 


J1>=e; 


NB. 


l=E^^i^E=?=li^e 


6 
5 


6       4 
7    4      3 


6     7 


liE^^E^Eiig^i^^lfe^lliili 


The  upward  progression  of  the  seventh  ia  the  next  to  the  last  measure 
(at  NB.),  is  conditioned  by  the  movement  of  the  Soprano. .    (See  page  84), 
The  treatment  of  the  cantus  firmus  in  the  Tenor  follows: 


^^^^ 


— u-3— f-^-f-r-r-f- 


i^m^^=i 


E^gEgggEE^ 


-* 


J4-^3I-0._g,. 


433. 


?ES£ 


IzcdiiB 


-|-2— g-^— 


9 T-« , 


P— (9 


_tiiiz:  — ^ ^^ — ^ 


^m 


:4=. 


gi!bigfei^sa5=M=i 


:q= 


MANUAL    OF   HARMONY. 


201 


©i^Ei 


£= 


m 


;i^i 


^^^s; 


^*-f 


cEB3 


Pil 


The  third  measure  gives  opportunity  to  speak  of  octave  and  fifth-succes- 
sion in  contrary  motion. 

According  to  the  principle  developed  on  page  27  and  the  following 
pages,  they  are  just  as  faulty  as  those  of  the  parallel  motion,  and  it  is  to 
be  especially  remarked  in  connection  with  octave-successions,  that  they 
confine  the  free  movement  of  the  voices ;  with  the  fifth-succcessions,  how- 
ever, the  character  of  separation  is  rendered  much  milder  by  contrary 
motion;  this  is  particularly  true  of  those  which  approach  each  other 
while  those  which  progress  from  each  other,  make  the  separation  or  want 
of  connection  more  perceptible.  (See  also  Example  No.  430  in  the  6th 
and  7th  measures,  between  Tenor  and  Bass). 

Compare  the  following  examples : 


434. 


^m^ 


m 


^ 


t=€m^Mm^ 


If  we  glance  at  the  treatments  found  in  this  chapter,  we  cannot  fail  to 
recognize  the  melodic  development  of  the  voices,  and  herein  lies  the  ground 
for  regarding  them  as  contrapuntal  labors  ;  for  exactly  in  this  consists  the 
essence  of  counterpoint,  in  distinction  from  the  purely  rhythmical-har- 
monic form,  viz.,  that  it  conditions  the  freer  melodic  leading  of  the  voices, 
but  with  observance  of  the  harmonic  laws,  which  latter  form,  as  it  were, 
its  innermost  substance. 

Everywhere  now  in  these  examples,  even  in  those  where  the  voices 
move  in  quarter  notes,  the  simply  harmonic  structure  can  be  demonstrated, 
and  thus  they  may  serve  the  purpose,  for  the  present,  of  making  us  under- 
stand the  difference  between  simply  harmonic  and  contrapuntal  treatment 
of  a  given  voice.  The  more  particular  discussion  of  this  can  only  be  taken 
up  in  connection  with  counterpoint  itself. 


202 


MANUAL    OF    HARMONY. 


CHAPTER    XXIV. 

The  Five-voiced  Movement 

As  the  doubling  of  the  intervals  of  a  triad  is  necessary  even  in  the 
four-voiced  movement,  so  in  five  and  more  than  five-voiced  movements  it 
becomes  a  necessity  in  a  still  greater  degree,  and  this  even  in  the  case  of 
the  chords  of  the  seventh. 

Since  in  the  pure  harmonic  movement,  each  voice  must  maintain  its 
independence,  those  intervals  especially  which  admit  of  a  double  progres- 
sion, will,  for  the  sake  of  attaining  this  independence,  be  capable  of  a 
reduplication.  This,  to  be  sure,  can  take  place  with  each  interval  of 
a  chord  under  certain  circumstances ;  the  seventh  will  be  least  adapted  for 
doubling,  except  where  a  melodic  leading,  as,  for  example,  in  passing,  ren- 
ders this  reduplication  necessary. 

Farther  remarks  follow  in  connection  with  the  examples  given. 


Exercise* 


6 
6     5 


4 
2     3 


435. 


ii^^S 


:t:: 


31=^ 


1 


In  the  treatment,  we  can  select,  according  to  the  position  of  the  voiceSi 
either  two  Sopranos,  two  Altos  or  two  Tenors. 


436. 

BOPBAKO. 

Alto  I. 
Alto  II. 
Tknob. 


m^^m 


B 


E^E^I^^lEg^ 


i^[| 


S <S—^-&- 


;i^Ef 


»=^j^ii^^^z^ 


Se^I 


pEIiEiEES 


6 
6      5 


4 
3    3 


-  \%m^kM^^^^^[l 


MANUAL    OF   HARMONS 

The  same  exercise  carried  out  in  another  manner  : 
a — ^-^ — s, — r_<9         — 


203 


437. 

80PSAN0  I 


80PRA.X0  II. 


Tkxor. 


— ; G* T~^^ 


1 


fc^E^ 


iHp 


;Ee; 


i 


Bass. 


b6 


4 
2  3 


ii^iii 


It  pertains  also   to  the  independence  of  the  voices,  that  two  voices  dc 

not  remain  stationary  upon  one  tone  or  in  the  octave,  if  the  chords  change. 

In  the  above  example,  this  is  the  case  in  the  first  and  second  measures 

between  the  second  Soprano  and  Tenor,  but  here  is  not  faulty,  becauso 

he  same  chord  only  leaves  its  position,  but  is  exchanged  for  no  other. 

The  following  case,  however  : 


43§. 


Irz: 


would  be  corrected  thus  : 


439. 


E^iil^liiiil^ 


I  I 


iiE^; 


:±: 


IIE 


i 


Remark. — ^This  rule  admits,  however,  of  frequent  exceptions  in  connection  with  poly- 
phonic movements,  because  there  other  relations  present  themselves. 

That  the  leading  of  the  voices  will  also  admit  of  the  doubling  of  the 
leading  tone,  is  shown  by  the  third  measure  of  Example  No.  437,  between 
the  second  Soprano  and  Tenor. 

As  in  the  four-voiced  movement,  so  here  in  a  still  greater  ilegree  in  the 


204 


MANUAL    OF   HARMONY. 


five  and  more  than  five-voiced  movement,  the  unavoidableness  of  covered 
fifths,  octaves  and  unisons  will  appear.  That  here  also  the  outer  voices 
must  progress  in  pure  relations,  and  a  greater  freedom  be  allowed  to  the 
middle  voices  only,  may  be  mentioned  again. 

The  following  example  contains  various  progressions  of  this  sort : 


440. 

80PBAN0  II. 

Alto  I. 
Alto  II. 
Tenob. 


-f2-___^. 


Babs. 


The  covered  fifth,  octave  and  unison  progressions  in  this  example  are 
indicated  by  strokes.  The  open  fifth  in  the  eighth  measure,  between  the 
second  Alto  and  Bass  is  not  to  be  avoided,  since  polyphonically  the  chord 
of  the  diminished  seventh  can,  only  with  difficulty,  be  made  to  progress 
otherwise. 

The  first  and  second  Altos  in  the  eighth  and  following  measures  could 
ftlso  be  made  to  progress  thus : 


441. 


(M. 


MANUAL    OF    HARMONY. 


205 


;e 


m 


1 


(N^=i=i^^ 


That  the  voices,  particularly  the  middle  voices,  must  often  cross  each 
I  other  is  shown  by  the  second  Alto  and  Tenor  in  the  second  and  third 
measures. 

For  practice  in  the  five-voiced  movement,  chorals  especially  can  be  used 
I       to  advantage. 

The  following  may  be  given  here  : 


Choral:    Alleln  Qott  in  der  Hoh'  sei  Ehr*. 

G  —       C  D    C  D. 


G      D. 


BS=i-gl=pi5Epl 


-G— (9- 


i^EEElEtEE: 


:tii?cz:i=n 


^~^: 


G     C 


W 


D       A 


E       ▲ 


B       B 


G     D 


A     —  G    D. 


lEE^|iigE^^|E^fE§^|ii,^te-:^| 


The  work  in  the  five  and  more  than  five-voiced  movement  requires  a 
simple  and  natural  Bass-progression,  and  the  less  artificial  and  difficult  the 
latter,  so  much  the  clearer  and  more  intelligible  the  succession  of  har- 
mony itself  will  become ;  this  is  here  the  more  important,  since  with  the 
fullness  of  the  chords  and  the  necessity  of  the  free  movement  of  the 
voices,  very  unintelligible  progressions  can  easily  arise. 

The  beginning  of  this  exercise  follows  here  : 

(5>  p  T   I   r-^  o  o  p  f  p  f 


443. 


#--; 


I 
I 

:p- 


I  \-r' 


r 


I     I 


I 


iPi 


G     G 


In  the  repetition,  the  following  succession  of  harmony  can  be  applied 


206 


MANUAL    OF   HARMONY. 


444. 


2     0 


CHAPTER    XXV. 

The  Six,  Seven  ami  Eight-voiced  Movement* 

The  necessity  of  doubling  or  trebling  increases  with  the  number  of  the 
voices  which  are  added ;  it  will  also  often  occur  in  connection  with 
an  independent  leading  of  the  voices,  that  the  voices  cross  each  other. 
The  simplest  harmonic  progressions  become  here,  in  a  still  greater  degree^ 
fundamental  condition  of  the  possibility  of  such  polyphonic  movements, 
and  it  must  be  remarked,  that  many  chords  are  not  adapted  at  all  for  this 
manner  of  writing,  because  their  intervals,  in  as  much  as  they  are  subject 
to  a  definite  progression,  do  not  allow  of  multiplication,  as,  for  example,  the 
altered  chords  and  the  diminished  chord  of  the  seventh. 

A  few  progressions  of  the  triad  may  follow  here. 

Progression  to  the  second  degree  : 


4-toiced : 


-<g — ^. — g- 


b-Toiced  : 


r=g: 


m 


<5 <5- 


EEEEEEEEz^EE 


:r-: 


:=S: 


invoiced : 


ee: 


445. 


HLOrHj^^IIL^ glZZ^: 


=:?:zi:a: 


-© — o — <s- 

•*k      —      1^ 


l-iDoicAd : 


MANUAL    OF    HARMONY. 


207 


Progression  to  the  third  degree  : 


i-Toiced . 


b-voiced . 


Q-voictd  : 


7'Voiced  : 


S-ToiceU: 


^— t— t-l=£=tij^=i:=t— J:-#: 


WM 


9- 


(2- 


1^^; 


gE^j; 


m^^^^m 


Progression  to  the  fourth  degree  : 

i-voiced :  b-voie.ed :  6-voiced :  7'Voice<i :  S-voiced: 


: — d.—Q E: 


-(2 fi- 

:f:zzi25: 


:_ «2: 


§•=1 


l?iiif 


:a— 


li 


;j 


Progression  to  the  j^^/i  degree  : 

^-voiced :  b-voiced :  ^-voiced : 


l-voiced : 


8'Voiced : 


ffl. 


-ii- 


We  pass  over  farther  combinations ;  to  try  them,  with  all  inversions,  will 
be  of  great  use. 

As  example  of  the  management  of  the  leading  of  the  voices,  the  choral 
found  under  No.  442,  may  follow  here  with  six  voices  : 


446. 

bopkano  i.  &  ii. 

Alto. 

Tbhob  I.  &  II. 
Bass. 


P 


"m: 


-h5>- 


I  I       I 


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z:lzx=rt:^l:±xi=it:ziiz:tizz:t-l 


:fz=F=lzT=r[:^; 


:=t: 


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r- 


» — -I — 35 m—^ — X >= — r — c^ o 


—I-, 


I         I 


ip|i#i^iii^g^i 


6 
6    5 


Pl^^^^^^^l^=^ 


MANUAL    OF   HARMONY. 


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w^^^mm 


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r 


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ri=^EEpp^g 


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4     -  6  7 

3     -  fl  6fl 

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MANVJ.L     OF   UARMONY. 
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4  3 


e^^H^i^l^ll^i^ 


Since  in  polyphonic  chorus-movements,  all  the  voices  do  not  always  work 
at  the  same  time,  as  in  a  choral-treatment,  the  movement  often  appears 
only  three  and  four-voiced,  and  receives  an  increase  of  intensity  through 
the  accession  of  a  numher  of  voices. 

The  following  examples  will  explain  this  kind  of  chorus-movement  and 
especially  serve  to  show,  that  in  polyphonic  work  also,  suspensions  and 
passing  notes  can  very  well  be  introduced,  without  detriment  to  the  clear 
/ess  and  intelligibility. 

447.  ~ 


SOPRAXO 
I&ll. 


Alto. 


Tkkof. 
l&il. 


Ba.39. 


|^  = 


\ — r 


z=::za: 


is:: 


:::^z: 


::j==lz[ 


its: 


isi^^lz 


ZSi- 


'.'srj. 


ff-3^^ 


J — I 


i-;-'    I 


^=: 


J*L_^ 


^H^iH 


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ilg^l^B^I^ 


■T-S T-«^5!n 


ffJ 


13: 


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r—v 


-6€h 


g_^ 


Ig^g^l^^l^fe^l^^ 


S^ 


4r-^ 


=^t^--i 


■■i— 4-,__j     ,1— J— I- 


FT^~ 


1^1 


i^-^?^^I^L^I?^lEEl^^ 


210 
44§. 

fiOPBANO  I. 


8OPBANO  II. 


MANUAL    OF   HARMONY. 
4S.  • 


Alto.  I. 


Alto  II, 


Texok. 


Bass. 


^—m 


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t^-^ 


t3: 


i^EE^'EEEi^ 


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fp^^ 


^^^^^=^^^^ 


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B 


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H 


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S: 


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MANUAL    OF    BARMONY. 


211 


't- 


n 


T~s: 


a 


i 


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m 


JE^ 


f— ^ 


i^^^^^^^^l 


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Hiii^^fi; 


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i 


In  eight-voiced  chorus-movements,  for  which,  as  a  rule,  the  customary 
four  voices  are  used  twice,  the  latter  are  not  always  found  employed  as 
eight  independent  voices,  which  would  easily  cause  too  great  fullness,  but 
frequently  two  voices  of  like  kind  are  employed  in  unison  (for  example,  two 
Sopranos,  two  Altos,  or  two  Tenors  and  two  Basses  in  unison),  so  that  the 
movement  often  appears  four,  five  and  six-voiced.  We  find  also  the  eight 
voices  divided  into  two  different  choirs,  which  work  each  for  itself,  and 
only  in  single  passages  together. 

As  an  example  of  the  particular  progression  which  many  of  these  voices 
must  make,  the  beginning  of  the  choral  given  above  may  follow  here  for 
eight  voices : 

449. 

SOPBASO   I.    &   II. 


Alto  I.  &  II. 


Tkkob  I.  &  II. 


Ba68  I.  &  II. 


6&=4|3iS^: 


=t:=t=i=P 


!=:?=; 


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lit: 


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^gn^n 


212 


MANUAL    OF  HARMONY. 


— TT-g— ^-f-F"^ 


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1 


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:t=.^ 


p=i^; 


i^i 


The  difficulty  of  this  manner  of  writing  is,  in  the  case  of  polyphonic 
movements  which  are  divided  into  two  diflferent  choirs,  met  by  this,  that 
where  two  or  more  choirs  work  together,  it  is  not  altogether  the  ionicdl 
difference,  but  often  the  metrical^  which  separates  the  voices  ;  it  is  always 
to  be  presumed,  however,  that  the  harmonic  succession  takes  place  in  the 
simplest  manner,  and  never  in  rapid  changes. 

The  above  is  generally  to  be  understood  when  we  speak  of  twelve  or  six- 
teen-voiced  choruses,  movements,  etc.,  and  single  pieces  of  Bach  only, 
are  found,  where  eight  and  more  voices  (among  which,  however,  instru 
mental  voices  are  to  be  reckoned),  are  treated  obligato. 

These  hints  concerning  the  polyphonic  movement  may  here  suffice,  since 
the  rest,  with  thorough  knowledge  of  harmony,  can  be  left  to  per- 
sonal study  and  the  inclination  for  polyphonic  movements.  Concerning 
its  application,  however,  we  may  farther  remark  that  the  use  of  the 
polyphonic  form  and  its  manner  of  treatment  above  shown,  will  have  appli- 
cation mostly  in  compositions  for  choirs ;  in  instrumental  music,  however, 
e.  g.,  in  orchestral  works,  will  not  find  place  (as  the  taking  part  of  so  many 
instruments  of  various  kinds  allows  us  to  suppose)  in  the  compass  adduced ; 
for  this  last,  in  the  majority  of  cases,  the  four-voiced  movement  will  bo 
sufficient,  concerning  the  farther  treatment  of  which  only  the  actual 
instruction  in  instrumentation  can  give  information,  since  here  the  rela- 
tions of  reduplication  (even  if  often  approaching  the  manner  shown  above), 
mast  still  be  subject  to  other  principles. 


MANUAL    OF   HARMONY. 


213 


CHAPTER  XXVI. 


On  the  Musical  Forms  of  Close, 

Several  kinds  of  close  have  already  been  mentioned  (pages  32  and  33) , 
in  relation  to  the  authentic  close,  farther  remarks  followed  on  pages  40 
and  53 ;  in  the  course  of  the  whole  treatise,  however,  no  farther  opportu- 
nity has  been  given  to  take  up  the  subject,  so  that  a  fuller  explanation  of 
these  and  other  kinds  of  close  may  here  follow  : 

The  forms  of  close  are  immediately  divided  into 

The  authentic  close  and 

The  plugalic  or  plagal  close. 

The  authentic  close  has  the  formula  V-I,  the  plagal  close  IV-I  (or  in 
minor  :  V-i,  iv-i),  as  was  before  remarked. 

Both  kinds  are  used  not  only  at  the  conclusions  of  whole  compositions, 
but  also  at  the  close  of  the  principal  parts,  of  the  periods,  and  their 
divisions.  The  more  particular  discussion  of  this  point  belongs  to  the 
doctrine  of  Form.     (See  the  book  referred  to,  page  142). 

If  the  plagal  close  concludes  a  piece,  it  seldom  stands  alone,  but  suc- 
ceeds the  authentic  close ;  in  a  composition  in  minor  it  also  frequently 
leads  to  major,  e.  g. 

I         1  .  auth.  plagal 

I      close 


450. 


ii 


i 


In  the  last  case,  as  in  the  above  example,  it  is  introduced  by  means  of  a 
modulation. 

The  closes  (cadences)  are  also  divided  into  ivhole  and  half  closes 
(cadences). 

By  the  first  is  understood  the  same  which  is  comprehended  under  the 
authentic  cadences.  In  the  case  of  the  whole  cadences  a  farther  distinction 
is  again  made  between  perfect  and  imperfect  ones. 

The  perfect  whole  cadences  are  those  in  which  the  Bass  receives  the 


214 


MANUAL    OF   HARMONY. 


fundamentals  of  the  dominant  and  tonic,  and  the  Soprano  the  fundamental 
of  the  tonic,  e.  g. 

not: 
451. 


gsfiij=j^=p=i 


If  this  is  not  the  case,  they  are  called  imperfect^  e.  g. 


452. 


^i^igEg^i^i^rB 


^     ^ 


&c. 


f^^^^^^^^i 


i 


If  the  Bass  progresses  from  the  dominant  to  another  degree,  they  are 
called  deceptive  cadences. 


453. 


^^iHiUF^i 


;i^^i: 


i 


See  the  examples,  pages  82  to  85. 

The  half-cadences  have  the  formula  I-V,  e.  g. 


454. 


;ee 


1^1 


V 


They  consist  therefore  in  this ;  that  the  dominant  triad  completes  the 
movement. 

Besides  the  tonic  triad,  other  chords  of  other  degrees  can  precede  the 
dominant  in  the  formaction  of  a  half-close,  e.  g. 


455. 


^Ef,|E^Epi:i^iE|^Er^  *.. 


IV 


G^  

<^  -ST 

TI  V 


Among  the  half-cadences  are  also  counted  those  closes  in  the  key  of  the 


MANUAL    OF    HARMONY.  215 

dominant  which  are  formed  by  a  modulation  into  the  same;  with  which, 
however,  the  modulation  itself  is  not,  in  a  definite  manner,  effected  through 
the  fundamental  position  of  the  dominant  harmony  of  the  seventh,  but 
fcither  through  its  inversions  or  through  the  chord  of  the  seventh  of  the 
seventh  degree,  e.  g. 

G:  viio^       I  g:  vii«»y  C:  V  c:  ii^^         V 

This  is,  however,  the  case  only  in  relation  to  the  ruling  key,  which  has 
immediately  before  been  made  use  of. 

For  the  farther  understanding  of  these  kinds  of  cadences,  compare  those 
which  are  found  in  the  examples  of  this  book. 

In  No.  388  is  found  in  the  third  and  fourth  measures  a  half  cadence 
formed  through  ii-V,  which  effects  the  close  of  the  first  division  of  the 
whole  period ;  in  the  seventh  and  eighth  measures,  however,  we  find 
a  perfect  ivhole  or  authentic  cadence. 

In  Example  No.  392  is  found  a  half  cadence,  in  the  third  and  fourth 
measures,  formed  through  I-V,  and  a  perfect  whole  or  authentic  cadence 
in  the  key  of  the  dominant  at  the  conclusion.  (Thus  this  is  no  half 
cadence,  since  the  dominant  harmony  of  the  seventh  renders  the  modular 
tion  decided). 

In  the  choral  treated  under  No.  446,  the  first  strophe  ends  with  an 
imperfect  whole  cadence,  the  second  with  2,  perfect  whole  cadence,  the 
third  with  a  AaZ/"-cadence  to  e  minor  (iv-V),  the  fourth  with  a  perfect 
whole  cadence  in  G  major,  the  fifth  with  Vkperfect  whole  cadence  in  a  minor, 
the  sixth  with  a  half  cadence  in  e  minor  (iv-V),  and  the  seventh  with 
a  perfect  whole  cadence  in  Gr  major. 

The  application  of  the  various  cadences  is  easily  found  in  chorals ;  for 
more  extended  pieces  they  form  the  means  of  boundary  and  connection 
of  the  smallest,  as  well  as  of  the  more  extended  movements,  and  are 
therefore  to  be  used  with  much  care,  because  upon  them  depends  a  great 
part  of  the  Form-construction  of  a  piece. 


INDEX  OF  SUBJECTS. 


Ae€<mpaniment,  figurated,  18S ;  harmonic  accompaniment  to  a  given  voice,  161 ;  17.J; 
195. 

After-striking  of  harmonic  tones,  121. 

Alto,  23 ;  alto  notes,  alto  clef,  1 18. 

Anticipation,  121. 

Arsis,  107,  138,  174. 

Bass,  23;  movement,  progression  of  the  same,  34,  36,  163,  206. 

By-tones,  harmonic,  128. 

Cadence,  55,  81 ;  whole,  half,  178,  213;  perfect,  imperfect,  62,  213;  in  connection  with 
modulation,  148. 

Cadence  formulce,  149,  150. 

Cantus  Jirmus,  195. 

C-clef,  113. 

Chorals,  as  exercises,  175,  205. 

Chords  21. 

Ckord-fomiations,  accidental,  105. 

Chords,  altered,  43,  91,  101;  passing,  138;  view  of  same,  99. 

see  also  Triads,  Chords  of  the  seventh. 

€hord  of  the  sixth  and  fourth,  48 ;  the  same  in  the  formation  of  the  close,  53 ;  in  con- 
nection with  modulation,  143;  as  passing  chord,  139 ;  use  of  the  same,  153. 

of  the  augmented  triad,  92,  198;  of  the  diminished  triad,  156,  188. 

i^Jhord  of  the  sixth  and  fifth,  59,  60,  62 ;  the  same  as  suspension,  189  ;  augmented,  97 ; 
in  connection  with  modulation,  147. 

€hord  of  the  second,  59,  61,  63. 

Chord  of  the  sixth,  fourth  and  second  (see  Chord  of  the  second). 

iChord  of  the  seventh,  21,  64;  dominant  chord  of  the  seventh,  64,  57,  61,  82,  144;  es. 
sential,  64 ;  the  same  in  passing,  138. 

—  of  the  seventh  degree  in  major,  68,  78,  90,  200. 

-— : diminished,  76,  79,  b7,  90;  in  connection  with  modulation,  146;  in  the  poly- 
phonic movement,  204. 

Chords  of  the  seventh,  connection  of  the  same  among  themselves,  73;  in  connection  with 
chords  of  other  tone  degrees,  81,  86 ;  view  of  the  same,  100. 

Chord  of  the  sixth,  47 ;  augmented,  94. 

Chord  of  the  thirteenth,  88,  90. 

Chord  of  the  fourth  and  third,  chord  of  the  sixth,  fourth  and  third,  69,  60,  62. 

Chord  of  the  eleventh,  88,  90. 

Chord  of  four  tones,  54  (see  chord  of  the  seventh). 

Chromatic  alteration,  91. 

Consonance,  17 ;  complete,  incomplete,  17. 

Contrary  motion,  26,  136. 


MANUAL    OF    UARMONY.  217 

Connection  of  chords,  '25,  73,  81 ;  local,  inner,  35. 
Close,  32;  authentic,  plagal,  32,  33. 

see  also  cadence,  whole  close,  half  close,  deceptive  cadence. 

Closing  cadence,  55,  81. 

Closing  formulae,  40,  41,  149. 
Cross-relation,  unharmonic,  16f . 

Deceptive  cadence,  %\ . 

Degrees,  diatonic,  13. 

Digression  (see  Modulation). 

Dissonance,  17. 

Dominant  harmony,  C-triad,  chord  of  the  seventh  in  connection  with  modulation,  144. 

JEleventh,  14. 

Exercises,  for  practice  of  the  primary  triads  in  major,  30 ;  of  all  triads  in  major,  37  ; 
of  the  triads  in  minor,  45  ;  of  the  inversions  of  the  triads,  49  ;  of  the  dominant  chord 
of  the  seventh,  58 ;  of  the  inversions  of  the  same,  03  ;  of  .the  secondary  chords  of 
the  seventh,  73 ;  of  the  connection  of  the  chords  of  the  seventh  among  themselves, 
74 ;  of  the  secondary  chords  of  the  seventh  in  minor,  77  ;  of  the  inversions  of  the 
same,  80 ;  of  the  deceptive  cadences,  85  ;  of  the  secondary  chords  of  the  seventh  in 
connection  with  chords  of  other  tone  degrees  or  keys,  87 ;  of  the  augmented  triad, 
94 ;  of  other  altered  chords,  98  ;  in  searching  out  modulation,  103  ;  of  the  suspen- 
sions, 112,  119;  of  the  harmonic  accompaniment  to  a  given  voice,  151,  152,  157, 
163,  164,  165,  170,  171, 172, 173;  in  the  development  of  melody,  177  ;  in  the  three- 
voiced  movement,  187,  191,  192;  of  the  two-voiced  movement,  193;  intheliarmo- 
nic  accompaniment  to  a  given  voice  in  melodic  development,  1 95,  200  ;  in  the  five- 
voiced  movement,  202,  205 

Fifteenth,  14. 

Ftfth,  13,  22 ;  perfect,  15,  16 ;  augmented,  15,  16,  75  ;  diminished,  15,  16,  38,  60;  fifth 
in  the  chord  of  the  seventh,  57,  70. 

Fifth-progressions  (parallel  fifths),  26,  28,  51,  79,  97;  open,  30,  78;  covered,  30,87, 
110,  158,  204;  in  connection  with  passing  and  changing  notes,  133;  in  contrary 
motion,  201.  .  , 

Figuring,  44,  48,  53,  54,  58,  63,  111,  128.  ^ 

Fourteenth,  14. 

Fourth,  13;  perfect,  augmented,  diminished,  15,  16;  preparation  of  the  perfect  fourth, 
155;  the  same  as  chord,  189,  196. 

Fourth-progressions  (fourth  parallels)  in  passing,  134,  136. 

Formation  of  the  close,  39,  63,  55. 

Fundamental  harmonies,  21 ;  chromatic  alterations  of  the  same,  91. 

Fundamental,  21 ;  in  the  chord  of  the  seventh,  57. 

Half  close  (half  cadence),  178,  213. 

Harmony,  21.  .  . 

Harmony,  tones  foreign  to  the,  105. 

Intervals,  division  of,  17  ;  view  of  the  same,  16,  18;  inversion  of  the  same,  38. 

see  also  omission,  reduplication. 

Intervals,  doctrine  of,  13. 

Interval,  13;  major,  perfect^  14;  minor,  augmented,  diminished,  15. 
Interval  steps  and  tkips,  augmented  and  diminished,  156. 
Intervals  above,  18. 
Intervals  bc^ow,  18. 


218  MAlflTAL    OF    HARMONY. 

Inversion,  47 ;  of  the  triads.  47 ;  of  the  chords  of  the  seventh,  59,  62,  18  j  (see  also  In- 
tervals). 

leading  tone,  3*7,  39,  56,  76,  116,  159,  203. 

Major  triad,  22,  65. 

Melody,  its  development,  116;  its  rhythmical  formation,  177. 

Middle  voices,  23. 

Minor  triad,  22,  33,  65. 

Modulation,  102  ;  means  for  the  same,  141 ;  its  extension  and  completion,  148. 

Movement,  one-voiced,  184;  two-voiced,  193;  three-voiced,  187;  four-voiced,  23;  five- 
voiced,  202 ;  six,  seven  and  eight-voiced,  206. 

Movement,  parallel,  contrary,  oblique,  26. 

Nachsatz,  177. 

Ninth,  14;  major,  minor,  15. 

Ninth,  chord  of  the,  88,  118,  127. 

Ninth-suspension,  118. 

Oblique  movement,  26. 

Octave,  13  ;  perfect,  augmented,  diminished,  15,  16. 

Octave-progressions  (octave  parallels),  26,  28;  open,  30,  110,  133;  covered,  30,  36,  63, 
84,  158,  203;  in  contrary  motion,  201. 

Omission  of  intervals,  57,  73,  188,  193. 

Organ-point,  123. 

Outer  voices,  11. 

Pass;  passing  notes,  128,  134. 

Passing  chords,  138. 

Period,  177. 

Plagal  close,  33,  41,  213. 

Position  of  the  chord,  close,  open,  dispersed,  31,  32,  114. 

Preparation,  of  the  seventh,  70;  of  the  suspension,  107. 

Prime,  13;  perfect,  augmented,  15,  16. 

Primary  chord  of  the  seventh,  54,  64. 

Primary  triads,  in  major,  23,  33;  in  minor,  40. 

Progression,  melodic,  unmelodic,  155, 156. 

of  the  secondary  chords  of  the  seventh,  66,  73,  81;  see  also  resolution,  bast, 

xmison,  octave,  fifth  progressions  <fec. ;  connection  of  the  chords. 

Reduplication,  of  intervals,  25,  39,  48,  58,  70,  95,  109,  111,  132,  202,  206. 

Resolution,  of  the  chord  of  the  dominant  seventh,  55,  60 ;  of  the  secondary  chords  of  the 
seventh  (in  major)  65;  (in  minor)  74;  of  the  suspension,  106,  109,  116,  120. 

Scale  (see  Triads). 

Secondary  triads,  in  major,  33  ;  in  minor,  42. 

Secondary  chords  of  the  seventh,  64,  78,  86. 

Second,  13;  major,  minor,  augmented,  15,  16. 

Second-progressions  (second  parallels),  in  passing,  134;  with  changing  notes,  186. 

Second,  step  of  the  augmented,  44. 

Sequence,  37. 

Seventh-progressions  (seventh  parallels),  in  passing,  134;  with  changing  notes,  136. 

Seventh,  13;  major,  minor,  diminished,  15,  16;  passing,  72,  176;  preparation,  70;  the 
same  without  preparation,  72,  77,  158,  164. 

SixtJi,  13;  major,  minor,  augmented,  15,  16. 

Signatures,  63. 

Soprano,  23;  soprano  notes,  soprano  clef,  113. 


MANUAL    OF    HARMONY,  219 

Stationary  voices,  128,  126. 

Sfriccture,  pure  harmonic,  24,  187. 

Style,  pure,  strict,  free,  24;  pure,  IST. 

Subdominant  triad,  23. 

Suspension,  105,  lOS  ;  m  the  h&as.  111;    from  below  upwards,  116;    in  several  voice*, 
117, 199. 

Tenth,  14. 

Tenor,  23 ;  tenor  notes,  tenor  clef,  113. 

Thesis,  107,  13S. 

ITiird,  13,  22;  major,  minor,  diminished,  15,  16;  in  the  chord  of  the  seventh,  156,  57 
70  (see  Leading  tone). 

Thirteenth,  14. 

Thorough-bass  notation  (see  Figurmg). 

Tonic  triad,  23,  142. 

Triad,  21 ;  major,  minor  22  ;  dominant  triad  (in  major)  23  ;  (in  minor)  40 ;  tonic  triad, 
23  ;  (in  connection  with  modulation)  142  ;  subdominant  triad,  23. 

double-diminished,  94 ;  harsh-diminished,  96,  96 ;  augmented,  43,  65,  92  ;  dimin- 
ished, 34,  38,  43,  50,  65. 

Triads,  of  the  major  scale,  21,  33,  43,  99. 

of  the  minor  scale,  40,  42,  46,  99 ;  natural  connection  of  the  same,  22 ;  view  of 

the  same,  46,  99. 

Tritonus,  70,  169. 

Twelfth,  14. 

Unison,  13. 

Unison  progressions,  27  ;  covered,  161,  206. 

Voices,  movement  of  the,  26,  55 ;  (see  Progression,  Ac). 

Voices,  compass  of  the,  113. 

Voices,  relation  of  the,  113. 

Voices,  outer,  23  ;  middle  voices,  23 ;  development  of  the  accompanying  voices,  145. 

Vordersatg,  174. 


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